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The value of x for which the matrix $\begin{vmatrix}-x&x&2\\2&x&-x\\x&-2&-x\end{vmatrix}$ will be non-singular, are |
$-2≤x≤-2$ for all x other than 2 and -2 $x >2$ $x ≤-2$ |
for all x other than 2 and -2 |
The given matrix will be non-singular, if $⇒\begin{vmatrix}-x&x&2\\2&x&-x\\x&-2&-x\end{vmatrix}≠0$ $⇒-x(-x^2-2x) -x (-2x+x^2)+2(-4-x^2) ≠0$ $⇒2x^2-8≠0⇒ x ≠ ±2$ |
