The value of x for which the matrix $\be

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

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

Options:

$-2≤x≤-2$

for all x other than 2 and -2

$x >2$

$x ≤-2$

Correct Answer:

for all x other than 2 and -2

Explanation:

The given matrix will be non-singular, if

$⇒\begin{vmatrix}-x&x&2\\2&x&-x\\x&-2&-x\end{vmatrix}≠0$

$⇒-x(-x^2-2x) -x (-2x+x^2)+2(-4-x^2) ≠0$

$⇒2x^2-8≠0⇒ x ≠ ±2$