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 A^t is its transpose matrix. Find:

(i) 2A + 3A^t (ii) 2A^t - 3A

(iii)  (iv) 

Solution 7

(i) 2A + 3A^t

(ii) 2A^t - 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 =