Question

Find the matrix of the co-factor for the following matrix.

`[(1,3),(4,-1)]`

Answer 1

Let A = `[(1,3),(4,-1)]`

Here, a₁₁ = 1, M₁₁ = − 1

∴ A₁₁ = (− 1)¹⁺¹(− 1) = − 1

a₁₂ = 3, M₁₂ = 4

∴ A₁₂ = (− 1)¹⁺²(4) = − 4

a₂₁ = 4, M₂₁ = 3

∴ A₂₁ = (− 1)²⁺¹(3) = − 3

a₂₂ = − 1, M₂₂ = 1

∴ A₂₂ = (− 1)²⁺²(1) = 1

∴ the co-factor matrix = `[("A"_11,"A"_12),("A"_21,"A"_22)]`

= `[(-1,-4),(-3,1)]`