Minor (linear Algebra) - Example

Example

For example, given the matrix

\begin{pmatrix} \,\,\,1 & 4 & 7 \\ \,\,\,3 & 0 & 5 \\ -1 & 9 & \!11 \\ \end{pmatrix}

suppose we wish to find the cofactor C23. The minor M23 is the determinant of the above matrix with row 2 and column 3 removed (the following is not standard notation):

\begin{vmatrix} \,\,1 & 4 & \Box\, \\ \,\Box & \Box & \Box\, \\ -1 & 9 & \Box\, \\ \end{vmatrix} yields \begin{vmatrix} \,\,\,1 & 4\, \\ -1 & 9\, \\ \end{vmatrix} = (9-(-4)) = 13

where the vertical bars around the matrix indicate that the determinant should be taken. Thus, C23 is (-1)2+3 M23

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