Question

If the matrix $\left[\begin{array}{cc}5x& 2\\ -10& 1\end{array}\right]$ is singular, find the value of x.

Answer 1

A matrix is said to be singular if its determinant is zero. Since the given matrix is singular, we get

$$\begin{gathered} A=\left[5x2 \\ -101\right] \\ \Rightarrow \left|A\right|=\left|5x2 \\ -101\right|=0 \\ \Rightarrow 5x+20=0\left[\mathrm{Expanding}\right] \\ \Rightarrow x=-\frac{20}{5}=-4 \end{gathered}$$