The determinant of a 3x3 matrix is computed by expanding along a row or column using cofactors. Which name describes this method?

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Multiple Choice

The determinant of a 3x3 matrix is computed by expanding along a row or column using cofactors. Which name describes this method?

Expanding a determinant along a row or column using cofactors is called cofactor expansion, also known as Laplace expansion. You select a row or column, multiply each entry by its cofactor (which is the sign-adjusted determinant of the corresponding 2×2 minor obtained by deleting that row and column), and sum the results. This exact method is described here, so the name cofactor expansion (Laplace expansion) is the correct label. Other techniques—such as the Sarrus rule for a quick 3×3 shortcut using diagonals, row-reduction to triangular form, or Gauss–Jordan for finding inverses—address different procedures and aren’t the process described by expanding along a row or column with cofactors.

Expanding a determinant along a row or column using cofactors is called cofactor expansion, also known as Laplace expansion. You select a row or column, multiply each entry by its cofactor (which is the sign-adjusted determinant of the corresponding 2×2 minor obtained by deleting that row and column), and sum the results. This exact method is described here, so the name cofactor expansion (Laplace expansion) is the correct label. Other techniques—such as the Sarrus rule for a quick 3×3 shortcut using diagonals, row-reduction to triangular form, or Gauss–Jordan for finding inverses—address different procedures and aren’t the process described by expanding along a row or column with cofactors.

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