Question

Solve the following equation for $x$ and $y$, if
$3x-y=\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]$ and $x-3y=\left[\begin{array}{cc}0& -1\\ 0& -1\end{array}\right]$

Answer 1

$3x-y=\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]$

Equation $\left(2\right)\times \left(3\right)$

$\Rightarrow 3x-9y=\left[\begin{array}{cc}0& -3\\ 0& -3\end{array}\right]$

$8y=\left[\begin{array}{cc}1& 2\\ -1& 4\end{array}\right]$

$\Rightarrow y=\left[\begin{array}{cc}1/8& 1/4\\ -1/8& 1/2\end{array}\right]$

Equation $\left(1\right)\times 3=9x-3y=\left[\begin{array}{cc}3& -3\\ -3& 3\end{array}\right]$

$x-3y=\left[\begin{array}{cc}0& -1\\ 0& -1\end{array}\right]$

$8x=\left[\begin{array}{cc}3& -2\\ -3& 4\end{array}\right]$

$\Rightarrow x=\left[\begin{array}{cc}3/8& -1/4\\ -3/8& 1/2\end{array}\right]$.