$$det(\left(\begin{matrix}-3&2&8\\1&2&2\\-4&1&-7\end{matrix}\right))$$

$$\left(\begin{matrix}-3&2&8&-3&2\\1&2&2&1&2\\-4&1&-7&-4&1\end{matrix}\right)$$

$$-3\times 2\left(-7\right)+2\times 2\left(-4\right)+8=34$$

$$-4\times 2\times 8+2\left(-3\right)-7\times 2=-84$$

$$34-\left(-84\right)$$

$$118$$

$$det(\left(\begin{matrix}-3&2&8\\1&2&2\\-4&1&-7\end{matrix}\right))$$

$$-3det(\left(\begin{matrix}2&2\\1&-7\end{matrix}\right))-2det(\left(\begin{matrix}1&2\\-4&-7\end{matrix}\right))+8det(\left(\begin{matrix}1&2\\-4&1\end{matrix}\right))$$

$$-3\left(2\left(-7\right)-2\right)-2\left(-7-\left(-4\times 2\right)\right)+8\left(1-\left(-4\times 2\right)\right)$$

$$-3\left(-16\right)-2+8\times 9$$

$$118$$

$A_{11}=\left|\begin{array}{rr}2 & 2 \\ 1 & -7\end{array}\right|=-16$

$A_{12}=-\left|\begin{array}{rr}1 & 2 \\ -4 & -7\end{array}\right|=-1$

$A_{13}=\left|\begin{array}{rr}1 & 2 \\ -4 & 1\end{array}\right|=9$

$A_{21}=-\left|\begin{array}{rr}2 & 8 \\ 1 & -7\end{array}\right|=22$

$A_{22}=\left|\begin{array}{rr}-3 & 8 \\ -4 & -7\end{array}\right|=53$

$A_{23}=-\left|\begin{array}{rr}-3 & 2 \\ -4 & 1\end{array}\right|=-5$

$A_{31}=\left|\begin{array}{rr}2 & 8 \\ 2 & 2\end{array}\right|=-12$

$A_{32}=-\left|\begin{array}{rr}-3 & 8 \\ 1 & 2\end{array}\right|=14$

$A_{33}=\left|\begin{array}{rr}-3 & 2 \\ 1 & 2\end{array}\right|=-8$

$\left[\begin{array}{rrr}-16 & -1 & 9 \\ 22 & 53 & -5 \\ -12 & 14 & -8\end{array}\right]$

$\left[\begin{array}{rrr}-16 & 22 & -12 \\ -1 & 53 & 14 \\ 9 & -5 & -8\end{array}\right]$