Question

If the value of determinant $\left|\begin{array}{cc}m& 2\\ -3& 7\end{array}\right|$ is $3$, find the value of $m$.

Answer 1

$\left|\begin{array}{cc}m& 2\\ -3& 7\end{array}\right|=3\left(\text{Given}\right)$

$\Rightarrow (m\times 7)-(2\times -3)=3$

$\Rightarrow 7m+6=3$

$\Rightarrow m=\frac{-3}{7}$

Hence the correct answer is $\frac{-3}{7}$.