Question

Given `3[(x, y),(z, w)] = [(x, 6),(-1, 2w)] + [(4, x + y),(z + w, 3)]` find the values of x, y, z and w.

Answer 1

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

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

Comparing the corresponding elements of these two matrices, we get:

3x = x + 4

⇒ 2x = 4

⇒ x = 2

3y = 6 + x + y

⇒ 2y = 6 + x

= 6 + 2

= 8

⇒ y = 4

3w = 2w + 3

⇒ w = 3

3z = –1 + z + w

⇒ 2z = –1 + w

= –1 + 3

= 2

⇒ z = 1

∴ x = 2, y = 4, z = 1 and w = 3