Question

For what value of x, the following matrix is singular?

$\left[\begin{array}{cc}5-x& x+1\\ 2& 4\end{array}\right]$

Answer 1

If a matrix A is singular, then $\left|A\right|=0$

$\therefore \left|\begin{array}{cc}5-x& x+1\\ 2& 4\end{array}\right|=0$

$$\begin{gathered} \Rightarrow 4(5-x)-2(x+1)0 \\ \Rightarrow 20-4x-2x-2 \\ \Rightarrow 18-6x=0 \\ \Rightarrow 18=6x \\ \Rightarrow x=3 \end{gathered}$$