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Question
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Solution
Let A = `[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Since A is a singular matrix,
|A| = 0
∴ `|(4, 3, 1),(7, "k", 1),(10, 9, 1)|` = 0
∴ 4(k – 9) – 3(7 – 10) + 1(63 – 10k) = 0
∴ 4k – 36 + 9 + 63 – 10k = 0
∴ –6k + 36 = 0
∴ 6k = 36
∴ k = 6
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