Definition:Cofactor/Examples

Examples of Cofactors
Let $D$ be the determinant defined as:


 * $D = \begin{vmatrix} a_{11} & a_{12} & a_{13} \\

a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{vmatrix}$

Then the cofactor of $a_{2 1}$ is defined as:

Let:
 * $D = \begin{vmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\

a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \\ a_{41} & a_{42} & a_{43} & a_{44} \\ \end{vmatrix}$

Let $D \left({2, 3 \mid 2, 4}\right)$ be an order-$2$ minor of $D$.

Then the cofactor of $D \left({2, 3 \mid 2, 4}\right)$ is given by: