Question

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

Answer 1

$$\begin{gathered} \left|\begin{array}{cc}m& 2\\ -5& 7\end{array}\right|=31 \\ \Rightarrow m\times 7-2\times \left(-5\right)=31 \\ \Rightarrow 7m+10=31 \\ \Rightarrow 7m=31-10 \\ \Rightarrow 7m=21 \\ \Rightarrow m=\frac{21}{7} \\ \therefore m=3 \end{gathered}$$