Question

Find the values of ‘x’, ‘y’, ‘z’ and ‘a’ which satisfy the following matrix equations:

`[(x + 3, 2y + x),(z - 1, 4a - 6)] = [(0, -7),(3, 2a)]`

Answer 1

By the definition of equality of matrices, we have

x + 3 = 0   ...(i)

2y + x = −7   ...(ii)

z − 1 = 3   ...(iii)

4a − 6 = 2a   ...(iv)

To find x and y,

From equation (i):

x = −3

Substitute x = −3 in (ii):

2y − 3= −7

2y = −4

y = `(-4)/2`

y = −2

From equation (iii):

z = 4

From equation (iv):

4a − 6 = 2a

4a − 6 = 2a

2a = 6

a = 3

Hence x = −3, y = −2, z = 4, a = 3