Cofactor/Examples/Arbitrary Example 1

Example of Cofactor

Let $D$ be the determinant defined as:

$D = \begin {vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end {vmatrix}$

Then the cofactor of $2$ is defined as:

\(\ds D_{12}\)

\(=\)

\(\ds \begin {vmatrix} 4 & 6 \\ 7 & 9 \end {vmatrix}\)

\(\ds \)

\(=\)

\(\ds \paren {-1}^{2 + 1} \paren {4 \times 9 - 6 \times 7}\)

\(\ds \)

\(=\)

\(\ds 6\)

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): cofactor or signed minor