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Question
If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if ______.
Options
λ = 2
λ ≠ 2
λ ≠ – 2
None of these
Solution
If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if none of these.
Explanation:
We have, A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`
⇒ |A| = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`
Expanding along R1 = `2|(2, 5),(1, 3)| lambda |(0, 5),(1, 3)| - 3|(0, 2),(1, 1)|`
= 2(6 – 5) – λ(0 – 5) – 3(0 – 2)
= 2 + 5λ + 6
= 8 + 5λ
If A–1 exists then |A| ≠ 0
∴ 8 + 5λ ≠ 0
So λ ≠ `(-8)/5`
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