Matrices and Determinants
4.0 Determinant of a square matrix
4.0 Determinant of a square matrix
Determinant of any orderLet $A = {\left[ {{a_{ij}}} \right]_n}$ be a square matrix $\left( {n > 1} \right)$.Determinant of $A$ is defined as the sum of products of elements of any one row (or any one column) with corresponding cofactors.
For square matrix $i=j$
Let $A = \left[ a \right]$ be a 1x1 marix.Determinant $A$ is defined as |$A$|=$a$.
Let $A = \left[ {\begin{array}{c} a&b \\ c&d \end{array}} \right]$ , then |A|is defined as ad-bc.
Example:
$A = \left| {\begin{array}{c} 5&3 \\ { - 1}&4 \end{array}} \right|$ = (5 X 4) - (-1 X 3) = 23
$\therefore $ |$A$|=23.
