Answer
The determinant is 18.
Work Step by Step
Consider the given matrix,
$A=\left[ \begin{array}{*{35}{r}}
4 & -1 & 3 \\
0 & 5 & -1 \\
5 & 2 & 4 \\
\end{array} \right]$
Therefore, the determinant of the matrix is
$\begin{align}
& \left| A \right|=\left| \begin{array}{*{35}{r}}
4 & -1 & 3 \\
0 & 5 & -1 \\
5 & 2 & 4 \\
\end{array} \right| \\
& =4\left( 20+2 \right)+1\left( 0+5 \right)+3\left( 0-25 \right) \\
& =88+5-75 \\
& =18
\end{align}$
The determinant of the matrix is $18$.
