- As per the given information it states,
$\left| \begin{matrix}
8 & 2 & 7 \\
12 & 3 & 5 \\
16 & 4 & 3 \\
\end{matrix} \right|$
Let $\vartriangle =\left| \begin{matrix}
8 & 2 & 7 \\
12 & 3 & 5 \\
16 & 4 & 3 \\
\end{matrix} \right|$
Now by applying row operation ${{R}_{3}}\to {{R}_{3}}-{{R}_{2}}$, we get
$\vartriangle =\left| \begin{matrix}
8 & 2 & 7 \\
12 & 3 & 5 \\
4 & 1 & -2 \\
\end{matrix} \right|$
Again apply row operation ${{R}_{2}}\to {{R}_{2}}-{{R}_{1}}$, we get
$\vartriangle =\left| \begin{matrix}
8 & 2 & 7 \\
4 & 1 & -2 \\
4 & 1 & -2 \\
\end{matrix} \right|$
As, ${{R}_{2}}={{R}_{3}}$, therefore the value of the determinants is zero.