Question

The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.

Options

• 5

• −23

• 3

• 23

Answer 1

The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is 5.

Explanation:

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

Cofactor of second row of matrix

i.e., A₂₁ = `-|(3, 2), (2, 1)|` = − (3 − 4) = 1

A₂₂ = `|(1, 2), (5, 1)|` = 1 − 10 = − 9

A₂₃ = `-|(1, 3), (5, 2)|` = − (2 − 15) = 13

∴ A₂₁ + A₂₂ + A₂₃ = 1 − 9 + 13 = 5