Question

If the value of the determinant $\left|\begin{array}{cc}m& 2\\ -5& 7\end{array}\right|$ is $31$, find $m$.

• A. $3$
• B. $8$
• C. $6$
• D. $2$

Answer 1

The correct option is A $3$

Given, $\left|\begin{array}{cc}m& 2\\ -5& 7\end{array}\right|$

$\Rightarrow 7m-(-10)=31$

$\Rightarrow 7m+10=31$

$\Rightarrow 7m=21$

$\Rightarrow m=3$