Question

Solve the following matrix equation for $x$ :

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

Answer 1

$\left[\begin{array}{ccc}x& -5& -1\end{array}\right]\left[\begin{array}{ccc}1& 0& 2\\ 0& 2& 1\\ 2& 0& 3\end{array}\right]\left[\begin{array}{c}x\\ 4\\ 1\end{array}\right]=\left[\begin{array}{c}0\end{array}\right]\left[\begin{array}{ccc}x& -5& -1\end{array}\right]\left[\begin{array}{c}x+2\\ 4\\ 2x+3\end{array}\right]=\left[\begin{array}{c}0\end{array}\right]\left[\begin{array}{ccc}{x}^2+2x& -45& -2x-3\end{array}\right]=\left[\begin{array}{c}0\end{array}\right]\left[\begin{array}{cc}{x}^2& -48\end{array}\right]=\left[\begin{array}{c}0\end{array}\right]x^2-48=0x^2=48x=\pm 4\sqrt{3}$