Question

How do you simplify determinants $?$

Answer 1

To simplify determinants:

A determinant can be simplified by using the following three methods:

1. Take a constant common factor from a row or column.
2. Interchange two rows or two columns.
3. Add or subtract a multiple of one row or column to the other row or column.

Suppose that $A$ is a $2\times 2$ matrix. Then the determinant of $A$ is given by:

$A=\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right|$

$\mathbf{\left|}\mathbf{A}\mathbf{\right|}\mathbf{}\mathbf{=}\mathbf{}{\mathit{a}}_{\mathbf{11}}\mathbf{\times }{\mathit{a}}_{\mathbf{22}}\mathbf{–}{\mathit{a}}_{\mathbf{21}}\mathbf{\times }{\mathit{a}}_{12}$

Where, $a_{11},a_{22},a_{21},$ and $a_{12}$ are elements of matrix $A$.

Hence, simplified form of determinant can be obtained .