Question

If $\Delta =\left|\begin{array}{ccc}5& 3& 8\\ 2& 0& 1\\ 1& 2& 3\end{array}\right|$, write the minor of the element $a_{23}.$

Answer 1

In linear algebra, a minor of a matrix is the determinant of some smaller square matrix, cut down from the original matrix by removing one or more of its rows or columns.

Since we need the minor of element $a_{23}$, the row II and column III would get cut.

The determinant of the remaining square matrix, i.e. $det\left[\begin{array}{cc}5& 3\\ 1& 2\end{array}\right]$ is the required minor.

$\therefore$ minor of $a_{23}=5\times 2-1\times 3=10-3=7.$