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Question
If λ = – 2, determine the value of `|(0, lambda, 1),(lambda^2, 0, 3lambda^2 + 1),(-1, 6lambda - 1, 0)|`
Solution
Let Δ = `|(0, lambda, 1),(lambda^2, 0, 3lambda^2 + 1),(-1, 6lambda - 1, 0)|`
Given λ = – 2
∴ Δ = `|(0, 2(-2), 1),((-2)^2, 0, 3(2)^2 + 1),(-1, 6(-2) - 1, 1)|`
= `|(0, -4, 1),(4, 0, 3 xx 4 + 1),(-1, -12 - 1, 0)|`
= `|(0, -4, 1),(4, 0, 13),(-1, -13, 0)|`
Expanding along the first row
Δ = 0 + 4[4 × 0 – (– 1)(13)] + [4 × – 13 – 0 × – 1]
= 4[0 + 13] + 1[– 52 + 0]
= 52 – 52
= 0
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