Question

If $\left[\begin{array}{ccc}1& 2& -1\\ 1& x-2& -1\\ x& 1& 1\end{array}\right]$ is singular, then the value of $x$ is

• A. 2
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (A)

Let $A=\left[\begin{array}{ccc}1& 2& -1\\ 1& x-2& 1\\ x& 1& 1\end{array}\right]$
if the matrix $A$ is singular, then $|A|=0$
$\left[\begin{array}{ccc}1& 2& -1\\ 1& x-2& 1\\ x& 1& 1\end{array}\right]=0$
Expand with respect to $R_1$
$\Rightarrow 1(x-2-1)-2(1-x)-1\left(1-x^2+2x\right)=0$
$\Rightarrow x-3-2+2x-1+x^2-2x=0$
$\Rightarrow x^2+x-6=0$
$\Rightarrow (x-2)(x+3)=0$
$\Rightarrow x=2,-3$