Question

Find the determinancof the matrix Q.

Answer 1

Using a Laplace expansion along the first column, we have

$\det Q=2\det\begin{bmatrix}2&1\\-1&6\end{bmatrix}+3\det\begin{bmatrix}3&4\\-1&6\end{bmatrix}+5\det\begin{bmatrix}3&4\\2&1\end{bmatrix}$

The determinant of a 2x2 matrix is trivial,

$\det\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc$

So we have

$\det Q=2\cdot13+3\cdot22+5\cdot(-5)=67$