• 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.