The cofactors of the elements of the first column of the matrix A = [20-1312-112] are ______. - Mathematics

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The cofactors of the elements of the first column of the matrix A = `[(2,0,-1),(3,1,2),(-1,1,2)]` are ______.

Options

  • 0, -7, 2

  • - 1, 3, - 2

  • 0, - 8, 4

  • (0, -1, 1)

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Solution

The cofactors of the elements of the first column of the matrix A = `[(2,0,-1),(3,1,2),(-1,1,2)]` are 0, - 1, 1.

Explanation:

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

Cofactor of the elements of first column of the matrix

A11 = `|(1,2),(1,2)|` = 2 - 2 = 0

A21 = `|(0,-1),(1,2)|` = - (0 + 1) = - 1

A31 = `|(0,-1),(1,2)|` = 0 + 1 = 1

∴ Cofactor is (0, -1, 1).

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