Question

Evaluate the determinant for the following matrix: [-4 -4 -3,3 3 -5,-5 2 -5]

Answer 1

Via a Laplace expansion across the first column, you have

$\begin{vmatrix}-4&-4&-3\\3&3&-5\\-5&2&5\end{vmatrix}=-4\begin{vmatrix}3&-5\\2&5\end{vmatrix}-3\begin{vmatrix}-4&-3\\2&5\end{vmatrix}-5\begin{vmatrix}-4&-3\\3&-5\end{vmatrix}$
$=-4(15-(-10))-3(-20-(-6))-5(20-(-9))$
$=-203$