Question

If P = `[(2, 6),(3, 9)]` and Q = `[(3, x),(y, 2)]`, find x and y such that PQ = null matrix.

Answer 1

Given:

P = `[(2, 6),(3, 9)]` and Q = `[(3, x),(y, 2)]`

∴ PQ = `[(2, 6),(3, 9)][(3, x),(y, 2)]`

= `[(2 xx 3 + 6 xx y, 2 xx x + 6 xx 2),(3 xx 3 + 9y, 3 xx x + 9 xx 2)]`

= `[(6 + 6y, 2x + 12),(9 + 9y, 3x + 18)]`

∵ PQ = Null matrix

∴ `[(6 + 6y, 2x + 12), (9 + 9y,  3x + 8)] = [(0, 0),(0, 0)]`

Comparing the corresponding elements, we have

6 + 6y = 0

`\implies` 6y = –6

`\implies` y = `(-6)/6` = –1

And 2x + 12 = 0

`\implies` 2x = –12

`\implies` x = `(-12)/2` = –6

Hence x = –6, y = –1.