Question

The value of $x$ for which the given matrix $\left[\begin{array}{ccc}-x& x& 2\\ 2& x& -x\\ x& -2& -x\end{array}\right]$ will be non -singular are

• A. $-2\le x\le 2$
• B. for all $x$ other than $2$ and $-2$
• C. $x\ge 2$
• D. $x\le -2$

Answer 1

The correct option is B for all $x$ other than $2$ and $-2$

Given $\left[\begin{array}{ccc}-x& x& 2\\ 2& x& -x\\ x& -2& -x\end{array}\right]$ is non singular .Hence the determinant should be non zero.

Determinant of the matrix is $-x({-x}^2-2x)+x({-x}^2+2x)+2(-4-x^2)=2x^2-8$

Now,$2x^2-8\ne 0\Rightarrow x^2\ne 4$

$\Rightarrow x\ne \pm 2$ ; Hence the matrix is non singular for all values of $x$ other than $2$ & $-2$.