Question

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

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

Answer 1

By the definition of equality of matrices, we have

x = 3   ...(i)

3x − y = 2   ...(ii)

2x + z = 4   ...(iii)

3y − a = 7   ...(iv)

Solve the equations

x = 3

Substitute x = 3 in (ii):

3(3) − y = 2

9 − y = 2

9 − 2 = y

y = 7

Substitute x = 3 in (iii):

2(3) + z = 4

6 + z = 4

z = 4 − 6

z = −2

Substitute y = 7 in (iv):

3(7) − a = 7

21 − a = 7

21 − 7 = a

a = 14

Hence, x = y = 7, z = −2, a = 14