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Question
Find K if the following matrices are singular.
`[("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)]`
Solution
Let A = `[("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)]`
Since A is a singular matrix,
|A| = 0
∴ `|("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)|` = 0
∴ (K – 1)(4 + 4) –2(12 –2) + 3(–6 – 1) = 0
∴ 8K – 8 – 20 – 21 = 0
∴ 8K = 49
∴ K = `(49)/(8)`.
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