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Question
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
Options
R
{4}
{0}
R – {4}
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Solution
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is R – {4}.
Explanation:
Given, matrix A = `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is a non-singular matrix.
∴ | A | ≠ 0
1(3 – a) – 2(2 – 3) + 1(2a – 9) ≠ 0
`\implies` 3 – a – 4 + 6 + 2a – 9 ≠ 0
`\implies` a – 4 ≠ 0
`\implies` a ≠ 4
∴ a ∈ A, such that A ∈ R – {4}.
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