Question

If `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse, then the real value of x is ______ 

Options

• 2

• 3

• 0

• 1

Answer 1

If `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse, then the real value of x is 1. 

Explanation:

Given `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse.

∴ `[(1, -1, x), (1, x, 1), (x, -1, 1)] = 0`

⇒ 1(x + 1) + 1(1 - x) + x(-1 - x²) = 0 

⇒ 2 - x - x³ = 0

⇒ x³ + x - 2 = 0

⇒ (x - 1) (x² + x + 2) = 0

⇒ x = 1