Let A = $\left[\begin{array}{cc}5-\mathit{x}& \mathit{x}+1\\ 2& 4\end{array}\right]$
It is given that the matrix A is singular, therefore |A| = 0
⇒ $\left|\begin{array}{cc}5-\mathit{x}& \mathit{x}+1\\ 2& 4\end{array}\right|$ = 0
⇒ 4(5 – x) – 2(x + 1) = 0
⇒ 20 – 4x – 2x – 2 = 0
⇒ -6x + 18 = 0
⇒ x = $\frac{-18}{-6}$ = 3
Thus, when x = 3, the given matrix A is singular.