SELINA Solutions for Class 10 Maths Chapter 9 - Matrices

Chapter 9 - Matrices Exercise Ex. 9(A)

Question 1

State, whether the following statements are true or false. If false, give a reason.

(i) If A and B are two matrices of orders 3 2 and 2 3 respectively; then their sum A + B is possible.

(ii) The matrices and are conformable for subtraction.

(iii) Transpose of a 2 1 matrix is a 2 1 matrix.

(iv) Transpose of a square matrix is a square matrix.

(v) A column matrix has many columns and one row.

Solution 1

(i) False

The sum A + B is possible when the order of both the matrices A and B are same.

(ii) True

(iii) False

Transpose of a 2 1 matrix is a 1 2 matrix.

(iv) True

(v) False

A column matrix has only one column and many rows.

Question 2

Given: , find x, y and z.

Solution 2

If two matrices are equal, then their corresponding elements are also equal. Therefore, we have:

x = 3,

y + 2 = 1 y = -1

z - 1 = 2 z = 3

Question 3

Solve for a, b and c if

(i)

(ii)

Solution 3

If two matrices are equal, then their corresponding elements are also equal.

(i)

a + 5 = 2 a = -3

-4 = b + 4 b = -8

2 = c - 1 c = 3

(ii) a= 3

a - b = -1

b = a + 1 = 4

b + c = 2

c = 2 - b = 2 - 4 = -2

Question 4

If A = and B = ; find: (i) A + B (ii) B - A

Solution 4

(i) A + B =

(ii) B - A

Question 5

If A=, B = and C = ; find:

(i) B + C (ii) A - C

(iii) A + B - C (iv) A - B +C

Solution 5

(i)B + C =

(ii)A - C =

(iii)A + B - C =

= =

(iv)A - B +C =

= =

Question 6

Wherever possible, write each of the following as a single matrix.

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 6

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

(iii) Addition is not possible, because both matrices are not of same order.

Question 7

Find, x and y from the following equations :

Solution 7

(i)

Equating the corresponding elements, we get,

3 - x = 7 and y + 2 = 2

Thus, we get, x = - 4 and y = 0.

(ii)

Equating the corresponding elements, we get,

-8 + y = -3 and x - 2 =2

Thus, we get, x = 4 and y = 5.

Question 8

Given: M =, find its transpose matrix Mt. If possible, find:

(i) M + Mt (ii) Mt - M

Solution 8

M =

Mt =

(i)

(i)

Question 9

Write the additive inverse of matrices A, B and C:

Where

Solution 9

We know additive inverse of a matrix is its negative.

Additive inverse of A =

Additive inverse of B =

Additive inverse of C =

Question 10

Given Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find the matrix X in each of the following:

(i) X + B = C - A

(ii) A - X = B + C

Solution 10

(i) X + B = C - A

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices


(ii) A - X = B + C

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 11

Given Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find the matrix X in each of the following:

(i) A + X = B

(ii) A - X = B

(iii) X - B = A

Solution 11

(i) A + X = B

X = B - A

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices


 

(ii) A - X = B

X = A - B

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 


 

(iii) X - B = A

X = A + B

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Chapter 9 - Matrices Exercise Ex. 9(B)

Question 1

Evaluate:

Solution 1

Question 2

Find x and y if:

Solution 2

Comparing the corresponding elements, we get,

12 + 2y = 10 and 3x - 6 = 0

Simplifying, we get, y = -1 and x = 2.

Comparing corresponding the elements, we get,

-x + 8 = 7 and 2x - 4y = -8

Simplifying, we get,

x = 1 and y = = 2.5

Question 3

Given ; find:

(i) 2A - 3B + C

(ii) A + 2C - B

Solution 3

(i) 2A - 3B + C

(ii) A + 2C - B

Question 4

Solution 4

Question 5

Given

(i) find the matrix 2A + B

(ii) find the matrix C such that:

C + B =

Solution 5

(i)

(ii) C + B =

C = - B =

Question 6

If ; find the values of x, y and z.

Solution 6

Comparing the corresponding elements, we get,

2x + 9 = -7 2x = -16 x = -8

3y = 15 y = 5

z = 9

Question 7

Given A = and At is its transpose matrix. Find:

(i) 2A + 3At (ii) 2At - 3A

(iii) (iv)

Solution 7

(i) 2A + 3At

(ii) 2At - 3A

(iii)

(iv)

Question 8

Given

Solve for matrix X:

(i) X + 2A = B

(ii) 3X + B + 2A = O

(iii) 3A - 2X = X - 2B.

Solution 8

(i) X + 2A = B

X = B - 2A

(ii) 3X + B + 2A = O

3X = -2A - B

(iii) 3A - 2X = X - 2B

3A + 2B = X + 2X

3X = 3A + 2B

Question 9

If , show that:

3M + 5N =

Solution 9

3M + 5N

Question 10

If I is the unit matrix of order 2 x 2; find the matrix M, such that:

(i) M - 2I =

(ii) 5M + 3I =

Solution 10

(i) M - 2I =

(ii) 5M + 3I =

Question 11

If

Solution 11

2M =

M =

Chapter 9 - Matrices Exercise Ex. 9(C)

Question 1

Evaluate: if possible:

Solution 1

The number of columns in the first matrix is not equal to the number of rows in the second matrix. Thus, the product is not possible.

Question 2

If and I is a unit matrix of order 2 2, find:

(i) AB (ii) BA (iii) AI

(iv) IB (v) A2 (vi) B2A

Solution 2

Question 3

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 

Question 4

Find x and y, if:

Solution 4

Comparing the corresponding elements, we get,

5x - 2 = 8 x = 2

20 + 3x = y y = 20 + 6 = 26

Comparing the corresponding elements, we get,

x = 2

-3 + y = -2 y = 1

Question 5

If , find:

(i) (AB)C (ii) A(BC)

Is A(BC) = (AB)C?

Solution 5

Hence, A(BC) = (AB)C.

Question 6

Given , find; if possible:

(i) AB (ii) BA (iii)A2

Solution 6

(iii) Product AA (=A2) is not possible as the number of columns of matrix A is not equal to its number of rows.

Question 7

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 

Question 8

If M = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices and I is a unit matrix of the same order as that of M; show that:

M2 = 2M + 3I

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Hence, M2 = 2M + 3I.


Question 9

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices and BA= M2, find the values of a and b.

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Given, BA = M2

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

a = 2 and  -2b = -2 Selina Solutions Icse Class 10 Mathematics Chapter - Matricesb = 1

Question 10

Given , find:

(i) A - B (ii) A2

(iii) AB (iv) A2 - AB + 2B

Solution 10

Question 11

If ; find:

(i) (A + B)2 (ii) A2 + B2

(iii) Is (A + B)2 = A2 + B2?

Solution 11

(iii) Clearly, (A + B)2 A2 + B2

Question 12

Find the matrix A, if B = and B2 = B + A.

Solution 12

B2 = B + A

A = B2 - B

A = 2(B2 - B)

Question 13

If A = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices and A2 = I; find a and b.

Solution 13

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

It is given that A2 = I.

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

1 + a = 1

Therefore, a = 0

 

 

 

-1 + b = 0 

Therfore, b = 1

Question 14

If ; then show that:

(i) A (B + C) = AB + AC

(ii) (B - A)C = BC - AC.

Solution 14

Question 15

If , simplify:

A2 + BC.

Solution 15

Question 16(i)

Solve for x and y:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 16(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 16(ii)

Solve for x and y:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 16(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 16(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 16(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 

Question 17

In each case given below, find:

(a) The order of matrix M.

(b) The matrix M.

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 17

We know, the product of two matrices is defined only when the number of columns of first matrix is equal to the number of rows of the second matrix.

 

(i) Let the order of matrix M be a x b.

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Clearly, the order of matrix M is 1 x 2.

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

a = 1 and a + 2b = 2 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 2b = 2 - 1 = 1 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices b = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

(ii) Let the order of matrix M be a x b.

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Clearly, the order of matrix M is 2 x 1.

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Comparing the corresponding elements, we get,

a + 4b = 13 ....(1)

2a + b = 5 ....(2)

 

Multiplying (2) by 4, we get,

8a + 4b = 20 ....(3)

 

Subtracting (1) from (3), we get,

7a = 7 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices a = 1

From (2), we get,

b = 5 - 2a = 5 - 2 = 3

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 18

If ; find the value of x, given that: A2 = B.

Solution 18

Question 19

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 19

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 20

If A and B are any two 2 x 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Solution 20

AB = BA = B

We know that I × B = B × I = B, where I is the identity matrix.

Hence, A is an identity matrix.

Question 21

Given Selina Solutions Icse Class 10 Mathematics Chapter - Matrices and that AB = A + B; find the values of a, b and c.

Solution 21

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

3a = 3 + a

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices2a = 3 

Selina Solutions Icse Class 10 Mathematics Chapter - Matricesa = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices           

 

 

3b = b Selina Solutions Icse Class 10 Mathematics Chapter - Matrices b = 0

4c = 4 + c Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 3c = 4 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices c = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 22

If , then compute:

(i) P2 - Q2 (ii) (P + Q) (P - Q)

Is (P + Q) (P - Q) = P2 - Q2 true for matrix algebra?

Solution 22

Clearly, it can be said that:

(P + Q) (P - Q) = P2 - Q2 not true for matrix algebra.

Question 23

Given the matrices:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices. Find:

(i) ABC (ii) ACB.

State whether ABC = ACB.

Solution 23

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Hence, ABC ≠ ACB.

Question 24

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find each of the following and state if they are equal:

(i) CA + B (ii) A + CB

Solution 24

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Thus, CA + B Selina Solutions Icse Class 10 Mathematics Chapter - Matrices  A + CB


Question 25

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find the matrix X such that AX = B.

Solution 25

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Clearly, the order of matrix X is 2 x 1.

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the two matrices, we get,

2x + y = 3 … (1)

x + 3y = -11 … (2)

Multiplying (1) with 3, we get,

6x + 3y = 9 … (3)

Subtracting (2) from (3), we get,

5x = 20

x = 4

From (1), we have:

y = 3 - 2x = 3 - 8 = -5

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 26

If, find (A - 2I) (A - 3I).

Solution 26

Question 27

If , find:

(i) At. A (ii) A. At

Where At is the transpose of matrix A.

Solution 27

Question 28

IfSelina Solutions Icse Class 10 Mathematics Chapter - Matrices, show that: 6M - M2 = 9I; where I is a 2 x 2 unit matrix.

Solution 28

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Hence, proved.


Question 29

IfSelina Solutions Icse Class 10 Mathematics Chapter - Matrices; find x and y such that PQ = null matrix.

Solution 29

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Comparing the corresponding elements, we get,

2x + 12 = 0

thus, x = -6

6 + 6y = 0

thus, y = -1

Question 30

Evaluate without using tables:

Solution 30

Question 31

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

(i) A + B = B + A

(ii) A - B = B - A

(iii) (B. C). A = B. (C. A)

(iv) (A + B). C = A. C + B. C

(v) A. (B - C) = A. B - A. C

(vi) (A - B). C = A. C - B. C

(vii) A2 - B2 = (A + B) (A - B)

(viii) (A - B)2 = A2 - 2A. B + B2

Solution 31

(i) True.

Addition of matrices is commutative.

(ii) False.

Subtraction of matrices is not commutative.

(iii) True.

Multiplication of matrices is associative.

(iv) True.

Multiplication of matrices is distributive over addition.

(v) True.

Multiplication of matrices is distributive over subtraction.

(vi) True.

Multiplication of matrices is distributive over subtraction.

(vii) False.

Laws of algebra for factorization and expansion are not applicable to matrices.

(viii) False.

Laws of algebra for factorization and expansion are not applicable to matrices.

Chapter 9 - Matrices Exercise Ex. 9(D)

Question 1

Find x and y, if:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

6x - 10 = 8

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices6x = 18

Selina Solutions Icse Class 10 Mathematics Chapter - Matricesx = 3

-2x + 14 = 4y

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices4y = -6+ 14 = 8

Selina Solutions Icse Class 10 Mathematics Chapter - Matricesy = 2

Question 2

Find x and y, if:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

3x + 18 = 15

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices3x = -3

Selina Solutions Icse Class 10 Mathematics Chapter - Matricesx = -1

12x + 77 = 10y

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices10y = -12 + 77 = 65

Selina Solutions Icse Class 10 Mathematics Chapter - Matricesy = 6.5

Question 3

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find x and y, if:

(i) x, y Î W (whole numbers)

(ii) x, y Î Z (integers)

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(i) x, y Î W (whole numbers)

It can be observed that the above two equations are satisfied when x = 3 and y = 4.

 

(ii) x, y Î Z (integers)

It can be observed that the above two equations are satisfied when x = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices3 and y = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices4.

Question 4

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

 

 

Solution 4

(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

 

 

(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

 

 

 

Question 5

Evaluate:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 6

IfSelina Solutions Icse Class 10 Mathematics Chapter - Matrices and 3A x M = 2B; find matrix M.

Solution 6

Let the order of matrix M be a x b.

 

3A x M = 2B

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Clearly, the order of matrix M is 2 x 1.


Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

-3y = -10


Selina Solutions Icse Class 10 Mathematics Chapter - Matrices y = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices          

12x - 9y = 12

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 7

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices, find the values of a, b and c.

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Comparing the corresponding elements, we get,

                                 

a + 1 = 5 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices a = 4

2 + b = 0 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices b = -2

-1 - c = 3 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices c = -4

Question 8

If A = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find:

(i) A (BA)

(ii) (AB). B

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 9

Find x and y, if: Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

5x = 5Selina Solutions Icse Class 10 Mathematics Chapter - Matricesx = 1

6y = 12Selina Solutions Icse Class 10 Mathematics Chapter - Matrices y = 2

Question 10

If matrix X =Selina Solutions Icse Class 10 Mathematics Chapter - Matrices and 2X - 3Y =Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find the matrix 'X' and 'Y'.

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 11

Given Selina Solutions Icse Class 10 Mathematics Chapter - Matrices; find the matrix X such that:

A + X = 2B + C

Solution 11

Given, A + X = 2B + C


Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 12

Find the value of x, given that A2 = B,

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 12

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Given, A2 = B


Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Comparing the corresponding elements, we get,

x = 36

Question 13

If Selina Solutions Icse Class 10 Mathematics Chapter - Matrices, and I is identity matrix of the same order and At is the transpose of matrix A, find At .B + BI

Solution 13

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 14

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 

Solution 14

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 15

LetSelina Solutions Icse Class 10 Mathematics Chapter - Matrices. Find A2 - A + BC.

Solution 15

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 16

Let A =Selina Solutions Icse Class 10 Mathematics Chapter - Matrices. Find A2 + AB + B2.

Solution 16

A = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

A2 = A Selina Solutions Icse Class 10 Mathematics Chapter - Matrices A = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

AB = A Selina Solutions Icse Class 10 Mathematics Chapter - Matrices B = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

=Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

B2 = B x B = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices A2 + AB + B2 = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 17

If Selina Solutions Icse Class 10 Mathematics Chapter - Matricesand 3A - 2C = 6B, find the values of a, b and c.

Solution 17

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

Comparing the corresponding elements, we get,

3a - 8 = 24 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 3a = 32 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices a = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

24 - 2b = 0 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 2b = 24 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices b = 12

11 = 6c Selina Solutions Icse Class 10 Mathematics Chapter - Matrices c = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 18

Given A =Selina Solutions Icse Class 10 Mathematics Chapter - Matrices.

Find the values of p and q.

Solution 18

A = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

BA = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

C2 = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

BA = C2 Selina Solutions Icse Class 10 Mathematics Chapter - MatricesSelina Solutions Icse Class 10 Mathematics Chapter - Matrices=Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

By comparing,

-2q = -8 Selina Solutions Icse Class 10 Mathematics Chapter - Matrices q = 4

And p = 8

Question 19

Given A =Selina Solutions Icse Class 10 Mathematics Chapter - Matrices . Find AB + 2C - 4D.

Solution 19

AB = Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Selina Solutions Icse Class 10 Mathematics Chapter - MatricesSelina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 20

Evaluate:

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 20

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

= Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 21

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

 

Solution 21

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

 

 

 

 

 

 

 

Question 22

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Solution 22

A2 = 9A + MI

A2 - 9A = mI ….(1)

Now, A2 = AA

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Substituting A2 in (1), we have

A2 - 9A = mI

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices 

Question 23

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

(i) Write the order of matrix X.

(ii) Find the matrix 'X'

Solution 23

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

 

(i) Let the order of matrix X = m × n

Order of matrix A = 2 × 2

Order of matrix B = 2 × 1

Now, AX = B

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices  

m = 2 and n = 1

 

Thus, order of matrix X = m × n = 2 × 1

 

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Multiplying (1) by 2, we get

4x + 2y = 8 ….(3)

Subtracting (2) from (3), we get

3x = 3

x = 1

Substituting the value of x in (1), we get

2(1) + y = 4

2 + y = 4

y = 2

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 24

Selina Solutions Icse Class 10 Mathematics Chapter - MatricesFind the matrix C where C is a 2 by 2 matrix. 

Solution 24

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Given: A2 - 5B2 = 5C

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

Question 25

Given matrix Selina Solutions Icse Class 10 Mathematics Chapter - Matrices. Find the matrix X if, X = B2 - 4B. Hence, solve for a and b given Selina Solutions Icse Class 10 Mathematics Chapter - Matrices.

Solution 25

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices

To find: a and b

Selina Solutions Icse Class 10 Mathematics Chapter - Matrices