Question

If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.

Options

• 1

• –1

• 0

• –2

Answer 1

If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is –2.

Explanation:

Consider, A = `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]`

So, |A| = `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]`

= α(9 – 2) – 14(6 – 6) – 1(4 – 18)

= 7α + 14

As, the inverse of matrix A does not exist.

Therefore, |A| = 0

`\implies` 7α + 14 = 0

Hence, α = – 2