Question

If $\left[1x1\right]\left[\begin{array}{ccc}1& 3& 2\\ 0& 5& 1\\ 0& 2& 0\end{array}\right]$ $\left[\begin{array}{c}1\\ 1\\ x\end{array}\right]=0$, then the values of $x$ are:

• A. $1,5$
• B. $-1,-5$
• C. $1,6$
• D. $-1,-6$
• E. $3,3$

Answer 1

The correct option is D $-1,-6$

Since, $\left[1x1\right]\left[\begin{array}{ccc}1& 3& 2\\ 0& 5& 1\\ 0& 2& 0\end{array}\right]$ $\left[\begin{array}{c}1\\ 1\\ x\end{array}\right]=0$

$\Rightarrow \left[\begin{array}{ccc}1& 3+5x+2& 2+x+0\end{array}\right]\left[\begin{array}{c}1\\ 1\\ x\end{array}\right]=0$

$\Rightarrow \left[\begin{array}{ccc}1& 5+5x& 2+x\end{array}\right]\left[\begin{array}{c}1\\ 1\\ x\end{array}\right]=0$
$\Rightarrow [1+5+5x+2x+x^2]=0$
$\Rightarrow x^2+7x+6=0$

$\Rightarrow x^2+6x+x+6=0$
$\Rightarrow (x+1)(x+6)=0$
$\therefore x=-1,-6$