Question

Using cofactors of elements of second row, evaluate |A|, where A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`

Answer 1

A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`

Cofactr of 2, A₂₁ = `(- 1)^(2 + 1)  |(3, 8),(2, 3)|`

= – [9 – 16]

= 7

Cofactr of 0, A₂₂ = `(- 1)^(2 + 2)  |(5, 8),(1, 3)|`

= 15 – 8

= 7

Cofactr of 1, A₂₃ = `(- 1)^(2 + 3)  |(5, 3),(1, 2)|`

= – [10 – 3]

= – 7

∴ |A| = a₂₁ A₂₁ + a₂₂ A₂₂ + a₂₃ A₂₃

= 2 × 7 + 0 × 7 + 1 × – 7

= 14 – 7

|A| = 7