Question

The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.

Options

• for all real values of λ 

• only for λ ≠ 0

• when λ ≠ 0 and λ ≠ –5

• only when λ ≠ –5

Answer 1

The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible when λ ≠ 0 and λ ≠ –5.

Explanation:

The given matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible.

∴ `|(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)| ≠ 0`

⇒ λ (3λ + 15) ≠ 0

⇒ λ ≠ 0 or λ ≠ –5