Question

If $\begin{bmatrix} {1}&{2} &{-1}\\ {1}&{x-2}& {-1} \\ {x}&{1}&{1}\\ \end{bmatrix} $ is singular, then the value of $x$ is

• A. 2
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (A)

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