Question

The value of $x,$ if $\left| \begin{matrix}

• x & 1 & 0 \ 1 & - x & 1 \ 0 & 1 & - x \end{matrix} \right| = 0$is equal to.

• A. $\pm \sqrt{6}$
• B. $\pm \sqrt{2}$
• C. $\pm \sqrt{3}$
• D. $\sqrt{2},\sqrt{3}$

Answer 1

Answer: (B)

$\pm \sqrt{2}$

Answer 2

We have $\Delta = \left| \begin{matrix}

• x & 1 & 0 \ 1 & - x & 1 \ 0 & 1 & - x \end{matrix} \right|$

$\Delta = - x(x^{2} - 1) - 1( - x - 0) = 0 \Rightarrow x = \pm \sqrt{2}$.