RD SHARMA Solutions for Class 12-science Maths Chapter 5 - Algebra of Matrices

Chapter 5 - Algebra of Matrices Exercise MCQ

Question 46

If A and B are symmetric matrices of the same order, then ABT - BAT is a

a. skew-symmetric matrix

b. null matrix

c. symmetric matrix

d. none of these

Solution 46

As A and B are symmetric matrices, we have

AT = A and BT = B … (i)

Consider,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Hence, ABT - BAT is a skew-symmetric matrix.

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. a null matrix

b. a unit matrix

c. -A

d. A

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3

If A and B are two matrices such that AB = A and BA = B, then B2 is equal to

 

a. B

b. A

c. 1

d. 0

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4

If AB = A and BA = B, where A and B are square matrices, then

 

a. B2 = B and A2 = A

b. B2 B and A2 = A

c. A2 A,B2 = B

d. A2A, B2 B

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5

If A and B are two matrices such that AB = B and BA =A, then A2 + B2 is equal to

 

a. 2 AB

b. 2 BA

c. A + B

d. AB

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

a. 3

b. 4

c. 6

d. 7

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 7

If the matrix AB is zero , then

 

a. It is not necessary that either A = 0 or B = 0

b. A = 0 or B = 0

c. A = O and B = 0

d. All the above statements are wrong

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

If A, B are square matrices of order 3, A is non-singular and AB = 0, then B is a

 

a. Null matrix

b. Singular matrix

c. Unit matrix

d. Non-singular matrix

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. B

b. nB

c. Bn

d. A + B

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

a. 0

b. -1

c. 2

d. None of these

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. a = 4, b = 1

b. a = 1, b = 4

c. a = 0, b = 4

d. a = 2, b = 4

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. 1 + α2 + βγ = 0

b. 1 - α2 + βγ = 0

c. 1 - α2 - βγ = 0

d. 1 + α2 - βγ = 0

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15

If S = [sij] is a scalar matrix such that sii = k and A is a square matrix of the same order, then AS = SA = ?

 

a. Ak

b. k + A

c. kA

d. kS

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16

If A is a square matrix such that A2 = A, then (I + A)3 - 7A is equal to

 

a. A

b. I - A

c. I

d. 3A

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17

If a matrix A is both symmetric and skew-symmetric, then

 

a. A is a diagonal matrix

b. A is a zero matrix

c. A is a scalar matrix

d. A is a square matrix

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. A skew-symmetric matrix

b. A symmetric matrix

c. A diagonal matrix

d. An upper triangular matrix

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 19

If A is a square matrix, then AA is a

 

a. Skew-symmetric matrix

b. Symmetric matrix

c. Diagonal matrix

d. None of these

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 20

If A and B are symmetric matrices, then ABA is

 

a. Symmetric matrix

b. Skew-symmetric matrix

c. Diagonal matrix

d. Scalar matrix

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. X = 0, y = 0

b. X + y = 5

c. X = y

d. None of these

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 22

If A is 3 × 4 matrix and B is a matrix such that ATB and BAT are both defined. Then, B is of the type

 

a. 3 × 4

b. 3 × 3

c. 4 × 4

d. 4 × 3

 

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 23

If A = [aij] is a square matrix of even order such that aij = i2 - j2, then

 

a. A is a skew - symmetric matrix and |A| = 0

b. A is symmetric matrix and |A| is a square

c. A is symmetric matrix and |A| = 0

d. None of these

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. none of these

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 26

Out of the following matrices, choose that matrix which is a scalar matrix:

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 27

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is

 

a. 27

b. 18

c. 81

d. 512

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 28

Which of the given values of x and y make the following pairs of matrices equal?

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. Not possible to find

 

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. -6, -12, -18

b. -6, 4, 9

c. -6, -4, -9

d. -6, 12, 18

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. I cos  θ + J sin θ

b. I sin θ + J cos θ

c. I cos θ - J sin θ

d. - I cos θ + J sin θ

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. 17

b. 25

c. 3

d. 12

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 32

If A = [aij] is a scalar matrix of order n × n such that aii = k for all I, then trace of A is equal to

 

a. nk

b. n + k

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

d. none of these

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. square matrix

b. diagonal matrix

c. unit matrix

d. none of these

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 34

The number of possible matrices of order 3 × 3 with each entry 2 or 0 is

 

a. 9

b. 27

c. 81

d. none of these

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. x = 3, y = 1

b. x = 2, y = 3

c. x = 2, y = 3

d. x = 3, y = 3

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 36

If A is a square matrix such that A2 = I, then (A - I)3 + (A + I)3 - 7A is equal to

 

a. A

b. I - A

c. I + A

d. 3A

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 37

If A and B are two matrix of order 3 × m and 3 × n respectively and m = n, then the order of 5A - 2B is

 

a. m × n

b. 3 × 3

c. m × n

d. 3 × n

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 38

If A is a matrix of order m × n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is

 

a. m × n

b. n × n

c. n × m

d. 3 × n

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 39

If A and B are matrices of the same order, then (ABT-BAT)T is a

 

a. skew-symmetric matrix

b. null matrix

c. unit matrix

d. symmetric matrix

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. I

b. A

c. O

d. -I  

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. I

b. 0

c. 2I

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 42

If A and B are square matrices of the same order, then (A + B) (A - B) is equal to

 

a. A2 - B2

b. A2 - BA - AB - B2

c. A2 - B2 + BA - AB

d. A2 - BA + B2 + AB

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Only AB is defined

b. Only BA is defined

c. AB ad BA both are defined

d. AB and BA both are not defined

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Diagonal matrix

b. Symmetric matrix

c. Skew-symmetric matrix

d. Scalar matrix

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

a. Identity matrix

b. Symmetric matrix

c. Skew-symmetric matrix

d. Diagonal matrix

Solution 45

Correct option: (d)

A matrix is called Diagonal matrix if all the elements, except those in the leading diagonal, are zero.

Chapter 5 - Algebra of Matrices Exercise Ex. 5.1

Question 1

If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?

Solution 1

We know that if a matrix is of the order Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices, it has mn elements. Thus, to find all the possible orders of a matrix having 8 elements, we have to find all the ordered pairs of natural numbers whose products is 8.

The ordered pairs are: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices are the ordered pairs of natural numbers whose product is 5.

Hence, the possible orders of a matrix having 5 elements are Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 5

Construct a 2 × 2 matrix A = [aij] whose elements aij are given by:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
 
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 5(vii)

Construct a 2 × 2 matrix A = [aij] whose elements aij are given by:

 

Aij = e2ix sin xj

Solution 5(vii)

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 6

Construct a 3 × 4 matrix A = [aij] whose elements aij are given by :

(i) aij = i + j

(ii) aij = i - j

(iii) aij = 2i

(iv) aij = j

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
 
(v)
 
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 14

 

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 18

The sales figure of two car dealer during january 2013 showed that dealer A sold 5 deluxe, 3 premium and 4 standard cars, while dealer B sold 7 deluxe, 2 premium and 3 standard cars. Total sales over the 2 month period of january - february revealed that dealer A sold 8 deluxe 7 premium and 6 standard cars. in the same 2 month period, dealer b sold 10 deluxe, 5 premium and 7 standard cars. Write 2 × 3 matrices summarizing for january and 2 - month period for each dealer.

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 21

Find the values of a and b if A = B, where

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Solution 21

As A = B,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Chapter 5 - Algebra of Matrices Exercise Ex. 5.2

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 15(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 15(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15(iii)

Find x, y satisfying the matrix equations

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 15(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 18

(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 18

(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Question 19(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 19(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 19(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 19(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 20

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 22

The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs. 15000 per month, find their monthly incomes using matrix method. This problem reflects which value?

Solution 22

Let 3x and 4x be the monthly incomes of Aryan and Babban respectively.

Let 5y and 7y be their monthly expenditures respectively.

As each individual saves Rs. 15000 per month, we have

3x - 5y = 15000 … (i)

4x - 7y = 15000 … (ii)

The above equations can be written in matrix form as follows

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Let AX = B, where Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Let's find A-1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Therefore, x = Rs. 30000 and y = Rs. 15000

So, monthly income of Aryan = Rs. 90,000 and monthly income of Babban is Rs. 120,000.

Chapter 5 - Algebra of Matrices Exercise Ex. 5.3

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 16(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 16(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 17(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 17(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 24(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 24(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 24(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 24(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Use this to find A4

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 40(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 40(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 40(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 40(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 40(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 40(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 48(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 48(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 48(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 48(ii)


Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 48(iii)

Find the matrix A such that

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 48(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 48(iv)

Find the matrix A such that

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 48(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Then show that (A + B)2 = A2 + B2.

 

Solution 51

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 52

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 53

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of MatricesRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 54(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 54(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 54(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 54(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 65(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 65(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 65(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 65(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 65(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 65(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 65(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 65(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 68

Let A and B be square matrices of the order 3 × 3.

Is (AB)2 = A2 B2? Give reasons.

Solution 68

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

 

 

 

Question 69

If A and B be square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.

 

Solution 69

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 70

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 70

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 71

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 71

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 72

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 72

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 73

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 73

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 74

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 74

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 75

To promote making of toilets for women, an organization tried to generate awareness through (i) house calls (ii) letters and (iii) announcements. The cost for each mode per attempt is given below:

 i. Rs. 50

 ii. Rs. 20

 iii. Rs. 40

The number of attempts made in three villages X, Y, and Z are given below:

 

 

(i)

(ii)

(iii)

X

400

300

100

Y

300

250

75

z

500

400

150

 

Find the total cost incurred by the organization for three villages separately, using matrices.

Solution 75

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 76

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, Calculate the total requirement of calories and proteins for each of the families. What awareness can you create among people about the planned diet from this question?

Solution 76

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 77

In a parliament election, a political party hired a public relations firm to promote its candidates in three ways - telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

The number of contacts of each type made in two cities X and Y is given in the matrix B as

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Find the total amount spent by the party in the two cities.

What should one consider before casting his/her vote - party's promotional activity or their social activities?

Solution 77

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 30

If A is a square matrix such that A2 = A, then find (2 + A)3 - 19A.

Solution 30

Given: A2 = A

(2 + A)3 - 19A

= 8I + A3 + 12A + 6A2 - 19A

= A3 + 6A2 - 7A + 8I

= A2 + 6A - 7A + 8I

= A - A + 8I

= 8I

Hence, (2 + A)3 - 19A = 8I.

Question 40(iv)

Solve the matrix equation:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Solution 40(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 48(v)

Find the matrix A such that

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Solution 48(v)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 48(vi)

Find the matrix A such that

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Solution 48(vi)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Solving equations (i) and (ii), we get, a1 = 1, b1 = -2

Solving (iii) and (iv), we get, a2 = 2, b2 = 0

From equations (v) and (vi), we get, a3 = -5, b3 = 4

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 50

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices and Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices find scalar k so that A2 + I = kA.

Solution 50

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices and Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

As A2 + I = kA

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Hence, k = -4.

Question 63

If A is a square matrix, using mathematical induction prove that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices for all n N.

Solution 63

To prove Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

For n = 1,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Therefore, it is true for n = 1.

Suppose the result is true for n = k

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Take n = k + 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Thus, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is true for all n N.

Question 78

The monthly incomes of Aryan and Babbar are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs. 15000 per month, find their monthly incomes using matrix method. This problem reflects which value?

Solution 78

Let 3x and 4x be the monthly incomes of Aryan and Babbar respectively.

Let 5y and 7y be their monthly expenditures respectively.

As each individual saves Rs. 15000 per month, we have

3x - 5y = 15000 … (i)

4x - 7y = 15000 … (ii)

The above equations can be written in matrix form as follows

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Let AX = B, where Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Let's find A-1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Therefore, x = Rs. 30000 and y = Rs. 15000

So, monthly income of Aryan = Rs. 90,000 and monthly income of Babbar is Rs. 120,000.

This encourages us to understand the power of savings and we should save certain money for future.

Question 79

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received Rs. 2800 as interest. However, if trust had interchanged money in bonds, they would have got Rs. 100 less as interest. Using matrix method, find the amount invested by the trust.

Solution 79

Let Rs. x and Rs. y is being invested in the first and second bonds respectively.

Let A be the investment matrix and B be the interest matrix.

Therefore, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

The annual interest = AB = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

If the interest had been interchanged, the total interest would be Rs. 100 less.

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Equations (i) and (ii) can be expressed as

PX = Q, where Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Now, |P| = 100 - 144 = -44

So, inverse of P exist.

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Thus, x = 10000 and y = 15000

Hence, the total amount invested is Rs. 25,000.

Chapter 5 - Algebra of Matrices Exercise Ex. 5.4

Question 1(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 1(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 3(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 3(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 3(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 3(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 3(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 3(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 6(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 6(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 6(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 6(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 10

If li, mi, ni ; i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Chapter 5 - Algebra of Matrices Exercise Ex. 5.5

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 9

For the matrix Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices find A + AT and verify that it is a symmetric matrix.

Solution 9

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Consider,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Thus, A + AT is a symmetric matrix.

Question 10

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is a symmetric matrix, then find the value of x.

Solution 10

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is a symmetric matrix, its transpose will be equal to itself.

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Hence, the value of x is 5.

Chapter 5 - Algebra of Matrices Exercise Ex. 5VSAQ

Question 64

Matrix Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is given to be symmetric, find the values of a and b.

Solution 64

As A is a symmetric matrix, we have

AT = A

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 65

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

Solution 65

Number of elements in a 2 × 2 matrix = 4

The first element can be 1, 2 or 3.

The second element can be 1, 2 or 3.

Similarly, the remaining two elements can take either of the 3 numbers.

So, for every element we have 3 choices.

Therefore, number of ways of writing 1, 2 or 3 in a 2 × 2 matrix is 34 which is 81.

Thus, the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3 is 81.

Question 66

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices then write the order of matrix A.

Solution 66

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Order of matrix P is 1 × 3

Order of matrix Q is 3 × 3

Order of matrix R is 3 × 1

After multiplying P and Q, we'll get an output matrix B of order 1 × 3.

After multiplying B with R, we'll get an output matrix of order 1 × 1.

Hence, the order of matrix A is 1 × 1.

Question 67

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is written as A = P + Q, whereas A = P + Q, where P is symmetric and Q is skew-symmetric matrix, then write the matrix P.

Solution 67

As P is symmetric, we have Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

As Q is skew-symmetric, we have Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Question 68

Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Write the order of matrix AB.

Solution 68

Matrix A is order 3 × 2

Matrix B is of order 2 × 4

Then the product matrix AB will have the order 3 × 4.

Question 69

If the matrix Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is skew-symmetric, find the values of 'a' and 'b'.

Solution 69

As matrix A is skew-symmetric

Therefore, -A = AT

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices 

Hence, the values of a and b are -2 and 3 respectively.

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 45

If ARd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices is written as B + C, where B is a symmetric matrix and C is a skew symmetric matrix, then find B.

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices
Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 49

If a matrix has 5 elements, write all possible orders it can have.

Solution 49

If a matrix is of order Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices, then the number of elements in the matrix is the product Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices.

Given that the required matrix is having 5 elements and 5 is a prime number.

Hence the prime factorization of 5 is either Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices.

Thus, the order of the matrix is either Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices.

Question 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 56

If A is a square matrix such that A2=A, then write the value of 7 A-(I+A)3, where I is the identity matrix.

Solution 56

A2 = A

A3 = A2 = A

7A - (I + A)3

= 7A - (I3 + A3 + 3A2I + 3AI2)

= 7A - (I + A + 3A + 3A)

= 7A - (I + 7A)

= -I

Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 60

Write 2×2 matrix which is both symmetric and skew-symmetric.

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 62

Construct a 2 × 2 matrix A = [aij] whose elements aij are given by

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

 

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Question 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices

Solution 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Algebra Of Matrices