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) 

(ii) 

(iii) 

Solution 6

(i) 

 

(ii) 

 

(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 M^t. If possible, find:

(i) M + M^t (ii) M^t - M

Solution 8

M =

M^t = 

(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 ; 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

(ii) A - X = B + C

Question 11

Given ; 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

 

(ii) A - X = B

X = A - B

 

 

(iii) X - B = A

X = A + B