Answer
$165$.
Work Step by Step
The given matrix is
$\begin{vmatrix}
8&2 &-1 \\
3 & 0 & 5\\
6 & -3 & 4
\end{vmatrix}$
The minors for the first column is
For $8$ the minor is
$\begin{vmatrix}
0 &5 \\
-3 & 4
\end{vmatrix}$
For $3$ the minor is
$\begin{vmatrix}
2 &-1\\
-3 & 4
\end{vmatrix}$
For $6$ the minor is
$\begin{vmatrix}
2 &-1\\
0 & 5
\end{vmatrix}$
Multiply each numerical factors of the column with corresponding minors as shown below.
$8\begin{vmatrix}
0 &5\\
-3 & 4
\end{vmatrix},3\begin{vmatrix}
2 &-1\\
-3 & 4
\end{vmatrix},6\begin{vmatrix}
2 &-1\\
0 & 5
\end{vmatrix}$.
Now add all three terms by changing the sign of the second term.
$=8\begin{vmatrix}
0 &5\\
-3 & 4
\end{vmatrix}-3\begin{vmatrix}
2 &-1\\
-3 & 4
\end{vmatrix}+6\begin{vmatrix}
2 &-1\\
0 & 5
\end{vmatrix}$.
Simplify.
$=8[(0)(4)-(-3)(5)]-3[(2)(4)-(-3)(-1)]+6[(2)(5)-(0)(-1)]$
Clear the parentheses.
$=8[0+15]-3[8-3]+6[10+0]$
Add like terms.
$=8[15]-3[5]+6[10]$
$=120-15+60$
$=120-15+60$
$=165$.
