Question

The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.

Options

• 17

• -16

• -17

• 16

Answer 1

The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = -17.

Explanation:

We have,

A = `[("a",-1,4),(-3,0,1),(-1,1,2)]`

A is not invertible

∴ |A| = 0

`|(a,-1,4),(-3,0,1),(-1,1,2)| = 0`

a(0 - 1) + 1(- 6 + 1) + 4(- 3 + 0) = 0

⇒ - a - 5 - 12 = 0

⇒ a = - 17