Question

If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A⁻¹ = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.

Options

• −15, −5

• −15, 5

• 15, −5

• 15, 5

Answer 1

−15, 5

Explanation:

We have,

A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A⁻¹ = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`

AA⁻¹ = l

∴ `[(2, 0, -1), (5, 1, 0), (0, 1, 3)] [(3, -1, 1), (α, 6, -5), (β, -2, 2)] = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

`[(6 - β, 0, 0), (15 + α, 1, 0), (α + 3β, 0, 1)] = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

∴ 6 − β = 1, 15 + α = 0

∴ β = 5, α = −15