Question
If $2\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right]+3\left[\begin{array}{ll}1 & 3 \\ y & 2\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right]$ Find the values of $x, y$ and $z.$
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Answer
$\begin{array}{l}2\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right]+3\left[\begin{array}{ll}1 & 3 \\ y & 2\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right] \end{array}$
$ {\left[\begin{array}{cc}6 & 2 x \\ 0 & 2\end{array}\right]+\left[\begin{array}{cc}3 & 9 \\ 3 y & 6\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right]} $
${\left[\begin{array}{cc}9 & 2 x+9 \\ 3 y & 8\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right]}$
comparing the correspinding elements we get
$2 x+9=-7 $
$\Rightarrow 2 x=-16 $
$\Rightarrow x=-8$
$3 y=15$
$\Rightarrow y=5$
$z=9$
$ {\left[\begin{array}{cc}6 & 2 x \\ 0 & 2\end{array}\right]+\left[\begin{array}{cc}3 & 9 \\ 3 y & 6\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right]} $
${\left[\begin{array}{cc}9 & 2 x+9 \\ 3 y & 8\end{array}\right]=\left[\begin{array}{cc}z & -7 \\ 15 & 8\end{array}\right]}$
comparing the correspinding elements we get
$2 x+9=-7 $
$\Rightarrow 2 x=-16 $
$\Rightarrow x=-8$
$3 y=15$
$\Rightarrow y=5$
$z=9$
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