Question

If the value of determinants $\left|\begin{array}{cc}x& -5\\ 3& 4\end{array}\right|$ is $31$, then find the value of $x$

Answer 1

We have, $\left|\begin{array}{cc}x& -5\\ 3& 4\end{array}\right|=31$
On solving, $4x-(-5)\left(3\right)=31$
$\Rightarrow 4x+15=31$
$\Rightarrow 4x=31-15$
$\Rightarrow x=\frac{16}{4}=4$
$\therefore x=4$