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