Question

If $\left[\begin{array}{ccc}1& x& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 0& 5& 1\\ 0& 3& 2\end{array}\right]\left[\begin{array}{c}x\\ 1\\ -2\end{array}\right]=0$, then the value of $x$ is

• A. 0
• B. $\frac{2}{3}$
• C. $\frac{5}{4}$
• D. $-\frac{4}{5}$

Answer 1

Answer: (C)

Given, $\left[\begin{array}{ccc}1& x& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 0& 5& 1\\ 0& 3& 2\end{array}\right]\left[\begin{array}{c}x\\ 1\\ -2\end{array}\right]=0$
$\Rightarrow [1\times 1]\left[\begin{array}{c}x+2-6\\ 0+5-2\\ 0+3-4\end{array}\right]=0$
$\Rightarrow [1\times 1]\left[\begin{array}{c}rx-4\\ 3\\ -1\end{array}\right]=0$
$\Rightarrow x-4+3x-1=0$
$\Rightarrow x=\frac{5}{4}$