$$det(\left(\begin{matrix}3&2&1\\4&5&6\\7&1&-2\end{matrix}\right))$$

$$\left(\begin{matrix}3&2&1&3&2\\4&5&6&4&5\\7&1&-2&7&1\end{matrix}\right)$$

$$3\times 5\left(-2\right)+2\times 6\times 7+4=58$$

$$7\times 5+6\times 3-2\times 4\times 2=37$$

$$58-37$$

$$21$$

$$det(\left(\begin{matrix}3&2&1\\4&5&6\\7&1&-2\end{matrix}\right))$$

$$3det(\left(\begin{matrix}5&6\\1&-2\end{matrix}\right))-2det(\left(\begin{matrix}4&6\\7&-2\end{matrix}\right))+det(\left(\begin{matrix}4&5\\7&1\end{matrix}\right))$$

$$3\left(5\left(-2\right)-6\right)-2\left(4\left(-2\right)-7\times 6\right)+4-7\times 5$$

$$3\left(-16\right)-2\left(-50\right)-31$$

$$21$$

$A_{11}=\left|\begin{array}{rr}5 & 6 \\ 1 & -2\end{array}\right|=-16$

$A_{12}=-\left|\begin{array}{rr}4 & 6 \\ 7 & -2\end{array}\right|=50$

$A_{13}=\left|\begin{array}{rr}4 & 5 \\ 7 & 1\end{array}\right|=-31$

$A_{21}=-\left|\begin{array}{rr}2 & 1 \\ 1 & -2\end{array}\right|=5$

$A_{22}=\left|\begin{array}{rr}3 & 1 \\ 7 & -2\end{array}\right|=-13$

$A_{23}=-\left|\begin{array}{rr}3 & 2 \\ 7 & 1\end{array}\right|=11$

$A_{31}=\left|\begin{array}{rr}2 & 1 \\ 5 & 6\end{array}\right|=7$

$A_{32}=-\left|\begin{array}{rr}3 & 1 \\ 4 & 6\end{array}\right|=-14$

$A_{33}=\left|\begin{array}{rr}3 & 2 \\ 4 & 5\end{array}\right|=7$

$\left[\begin{array}{rrr}-16 & 50 & -31 \\ 5 & -13 & 11 \\ 7 & -14 & 7\end{array}\right]$

$\left[\begin{array}{rrr}-16 & 5 & 7 \\ 50 & -13 & -14 \\ -31 & 11 & 7\end{array}\right]$