Question

Evaluate the following determinant:

\[\begin{vmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{vmatrix}\]

Answer 1

\[∆ = \begin{vmatrix}1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2\end{vmatrix}\]
\[ = 1\begin{vmatrix}- 1 & 2 \\ 5 & 2\end{vmatrix} - ( - 3)\begin{vmatrix}4 & 2 \\ 3 & 2\end{vmatrix} + 2\begin{vmatrix}4 & - 1 \\ 3 & 5\end{vmatrix}\]
\[ = 1\left( - 2 - 10 \right) + 3\left( 8 - 6 \right) + 2\left( 20 + 3 \right)\]
\[ = ( - 12) + 6 + 46\]
\[ = 40\]