Answer
The value of $x$ is, $=3$
Work Step by Step
Consider, $\left| \begin{matrix}
2 & x & 1 \\
-3 & 1 & 0 \\
2 & 1 & 4 \\
\end{matrix} \right|=39$
Evaluate the above determinant as follows:
$\left| \begin{matrix}
2 & x & 1 \\
-3 & 1 & 0 \\
2 & 1 & 4 \\
\end{matrix} \right|=39$
Evaluate the above determinant by expanding along the first row as follows:
$2\left| \begin{matrix}
1 & 0 \\
1 & 4 \\
\end{matrix} \right|-x\left| \begin{matrix}
-3 & 0 \\
2 & 4 \\
\end{matrix} \right|+1\left| \begin{matrix}
-3 & 1 \\
2 & 1 \\
\end{matrix} \right|=39$
Next, calculate the above determinant as follows:
$\begin{align}
& 2\left( 4-0 \right)-x\left( -12-0 \right)+\left( -3-2 \right)=39 \\
& 8+12x-5=39 \\
& 12x+3=39
\end{align}$
Add $-3$ to both sides to get,
$12x=36$
Divide by $12$. Now,
$x=3$.
Therefore, $x=3$
