Answer
The value is 48.
Work Step by Step
Expand along row 1,
$\left| \begin{matrix}
2 & 0 & 0 & 0 & 0 \\
0 & 3 & 0 & 0 & 0 \\
0 & 0 & 2 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 4 \\
\end{matrix} \right|=2\left| \begin{matrix}
3 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 4 \\
\end{matrix} \right|\text{ (as other terms are zero)}$
Again, expand along row 1
$2\left| \begin{matrix}
3 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 4 \\
\end{matrix} \right|\text{= 2}\cdot \text{3}\left| \begin{matrix}
2 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 4 \\
\end{matrix}\text{ } \right|\text{(as other terms are zero)}$
Again, expand along row 1
$\begin{align}
& \text{2}\cdot \text{3}\left| \begin{matrix}
2 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 4 \\
\end{matrix}\text{ } \right|\text{=2}\cdot 3\cdot 2\left| \begin{matrix}
1 & 0 \\
0 & 4 \\
\end{matrix} \right|\text{(as other terms are zero)} \\
& \text{ =2}\cdot 3\cdot 2(1\cdot 4-0) \\
& \text{ =2}\cdot 3\cdot 2\cdot 4 \\
& \text{ =48} \\
\end{align}$
So the solution of given determinant is 48.
