Answer
16
Work Step by Step
First, use cofactor expansion (Theorem 4.1) along the first row:
\[
\begin{vmatrix}
1 & 0 & 3\\5 & 1 & 1\\0 & 1 & 2
\end{vmatrix}
=
1 \cdot
\begin{vmatrix}
1 & 1\\1 & 2
\end{vmatrix}
-0+3 \cdot
\begin{vmatrix}
5 & 1\\0 & 1
\end{vmatrix}
\]
Then simplify the expansion:
$=1 \cdot (2-1) + 3 \cdot (5-0)$
$=1+15$
$=16$