Question

If $\left[234\right]\left[\begin{array}{ccc}1& x& 3\\ 2& 4& 5\\ 3& 2& x\end{array}\right]\left[\begin{array}{c}x\\ 2\\ 0\end{array}\right]=0$, then $x=$ ________.

• A. $\frac{7}{3}$
• B. $\frac{5}{3}$
• C. $-\frac{5}{3}$
• D. $-\frac{7}{3}$

Answer 1

The correct option is C $-\frac{5}{3}$

Given, $\left[234\right]\left[\begin{array}{ccc}1& x& 3\\ 2& 4& 5\\ 3& 2& x\end{array}\right]\left[\begin{array}{c}x\\ 2\\ 0\end{array}\right]=0$

$\left[\begin{array}{ccc}20& 20+2x& 21+4x\end{array}\right]\left[\begin{array}{c}x\\ 2\\ 0\end{array}\right]=0$

$\Rightarrow 20x+40+4x=0$
$\Rightarrow 24x+40=0$
$\Rightarrow x=-\frac{5}{3}$