$$[\begin{matrix}1&3&1\\ 0&-11&-3\\ 1&5-1\end{matrix}]$$
$14$
$$det(\left(\begin{matrix}1&3&1\\0&-11&-3\\1&4&0\end{matrix}\right))$$
$$\left(\begin{matrix}1&3&1&1&3\\0&-11&-3&0&-11\\1&4&0&1&4\end{matrix}\right)$$
$$3\left(-3\right)=-9$$
$$-11+4\left(-3\right)=-23$$
$$-9-\left(-23\right)$$
$$14$$
$$det(\left(\begin{matrix}-11&-3\\4&0\end{matrix}\right))-3det(\left(\begin{matrix}0&-3\\1&0\end{matrix}\right))+det(\left(\begin{matrix}0&-11\\1&4\end{matrix}\right))$$
$$-4\left(-3\right)-3\left(-\left(-3\right)\right)-\left(-11\right)$$
$$12-3\times 3+11$$
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$\left(\begin{matrix}1&3&1\\0&-11&-3\\1&4&0\end{matrix}\right)$
