Selina Solutions Concise Maths Class 10 Chapter 9 Matrices

 

Selina Solutions Concise Maths Class 10 Chapter 9 Matrices

Salina Maths class 10 solutions Class 10 Chapter 9 Matrices have been provided to you through an online medium, using which you can understand the difficult questions of ICSE Class 10 Mathematics, and can prepare for the upcoming Board exam.

Selina Class 10 ICSE solution will give strength to you and the board will also clear the exam, Mathematics Subject demands time and practice, then keep practicing and you will definitely get success.

Exercise 9(A) Solutions

Exercise 9(B) Solutions

Exercise 9(C) Solutions

Exercise 9(D) Solutions

Selina Solutions Concise Maths Class 10 Chapter 9 Matrices Exercise 9(C)

Question 1. Evaluate: if possible:

If not possible, give reason.

Solution:

= [6 + 0] = [6]

= [-2+2 3-8] = [0 -5]

=

The multiplication of these matrices is not possible as the rule for the number of columns in the first is not equal to the number of rows in the second matrix.

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

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

(iv) IB (v) A2 (iv) B2A

Solution:

(i) AB 

(ii) BA 

(iii) AI 

(iv) IB

(v) A2 

(vi) B2 

B2A 

Question 3. If  find x and y when x and y when A2 = B.

Solution:

A2 

A2 = B

On comparing corresponding elements, we have

4x = 16

x = 4

And,

1 = -y

y = -1

Question 4. Find x and y, if:

Solution:

(i)

On comparing the corresponding terms, we have

5x – 2 = 8

5x = 10

x = 2

And,

20 + 3x = y

20 + 3(2) = y

20 + 6 = y

y = 26

(ii)

On comparing the corresponding terms, we have

x = 2

And,

-3 + y = -2

y = 3 – 2 = 1

Question 5. 

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

Solution:

(i) (AB)

(AB) C

(ii) BC

A (BC)

Therefore, its seen that (AB) C = A (BC)

Question 6.  is the following possible:

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

Solution:

(i) AB

(ii) BA

(iii) A2 = A x A, is not possible since the number of columns of matrix A is not equal to its number of rows.

Question 7.  Find A2 + AC – 5B.

Solution:

A2

AC

5B

A2 + AC – 5B =

Question 8. If  and I is a unit matrix of the same order as that of M; show that:

M2 = 2M + 3I

Solution:

M2

2M + 3I

Thus, M2 = 2M + 3I

Question 9.  and BA = M2, find the values of a and b.

Solution:

BA

M2

So, BA =M2

On comparing the corresponding elements, we have

-2b = -2

b = 1

And,

a = 2

Question 10. 

(i) A – B (ii) A2 (iii) AB (iv) A2 – AB + 2B

Solution:

(i) A – B

(ii) A2

(iii) AB

(iv) A2 – AB + 2B =

Question 11. 

(i) (A + B)2 (ii) A2 + B2

(iii) Is (A + B)2 = A2 + B2 ?

Solution:

(i) (A + B)

So, (A + B)2 = (A + B)(A + B) =

(ii) A2

B2

A2 + B2

Thus, its seen that (A + B)2 ≠ A2 + B2+

Question 12. Find the matrix A, if B =  and B2 = B + ½A.

Solution:

B2

B2 = B + ½A

½A = B2 – B

A = 2(B2 – B)

Question 13. If  and A2 = I, find a and b.

Solution:

A2

And, given A2 = I

So on comparing the corresponding terms, we have

1 + a = 1

Thus, a = 0

And, -1 + b = 0

Thus, b = 1

Question 14. If  then show that:

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

(ii) (B – A)C = BC – AC.

Solution:

(i) A(B + C)

AB + AC

Thus, A(B + C) = AB + AC

(ii) (B – A)C

BC – AC

Thus, (B – A)C = BC – AC

Question 15. If  simplify: A2 + BC.

Solution:

A2 + BC

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