Question

If $\left[\begin{array}{ccc}2+x& 3& 4\\ 1& -1& 2\\ x& 1& -5\end{array}\right]$ is a singular matrix, then $x$ is

• A. $\frac{13}{25}$
• B. $\frac{-25}{13}$
• C. $\frac{5}{13}$
• D. $\frac{25}{13}$

Answer 1

Answer: (B)

$\frac{-25}{13}$

Since $\left[\begin{array}{ccc}2+x& 3& 4\\ 1& -1& 2\\ x& 1& -5\end{array}\right]$ is a singular matrix
$\therefore \left|\begin{array}{ccc}2+x& 3& 4\\ 1& -1& 2\\ x& 1& -5\end{array}\right|=0$
$\Rightarrow$ $(2+x)(5-2)-3(-5-2x)+4(1+x)=0$
$\Rightarrow$ $6+3x+15+6x+4+4x=0$
$\Rightarrow$ $13x+25=0$
$\Rightarrow$ $x=-\frac{25}{13}$