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

Answer 1

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`