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Question
Answer the following question:
If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
Solution
AB = `[(1, 2),(3, 2),(-1, 0)] [(1, 3, 2),(4, -1, -3)]`
`[(1 + 8, 3 - 2, 2 - 6),(3 + 8, 9 - 2, 6 - 6),(-1 + 0, -3 + 0, -2 + 0)]`
= `[(9 , 1, -4),(11, 7, 0),(-1, -3, -2)]`
∴ |AB| = `|(9, 1, -4),(11, 7, 0),(-1, -3, -2)|`
= 9 (– 14 + 0) –1(–22 + 0) – 4(–33 + 7)
= –126 + 22 + 104
= 0
∴ AB is a singular matrix.
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