Question

Find the value of $x$ for which the matrix
$A=\left[\begin{array}{ccc}3-x& 2& 2\\ 2& 4-x& 1\\ -2& -4& -1-x\end{array}\right]$ is singular.

• A. $0,1$
• B. $1,3$
• C. $0,3$
• D. $3,2$

Answer 1

Answer: (C)

$\left|A\right|=\left[\begin{array}{ccc}3-x& 2& 2\\ 2& 4-x& 1\\ -2& -4& -1-x\end{array}\right]=0$

$\Rightarrow {\left(x-3\right)}^{2}x=0\Rightarrow x=0,3.$