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Question
Find k if the following matrix is singular:
`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
Solution
Let C = `[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
Since C is a singular matrix, ICI = 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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