Question

Find $x$, if $\left[\begin{array}{ccc}1& 2& x\\ 1& 1& 1\\ 2& 1& -1\end{array}\right]$ is singular.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

For singular matrix, $|A|=0$
$\therefore \left[\begin{array}{ccc}1& 2& x\\ 1& 1& 1\\ 2& 1& -1\end{array}\right]=0$
$\Rightarrow 1\left(-1-1\right)-2\left(-1-2\right)+x\left(1-2\right)=0$
$\Rightarrow -2+6-x=0\Rightarrow x=4$