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Question
Determine the values of a and b so that the following matrices are singular:
B = `[("b" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
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Solution
B = `[("b" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
|B| = `[("b" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
= (b – 1 )(4 + 4) – 2(12 – 2) + 3(– 6 – 1)
= 8(b – 1) – 20 – 21
= 8b – 8 – 41
|B| = 8b -49
Given that B is singular
∴ |B| = 0
8b – 49 = 0
⇒ b = `49/8`
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