Question
Find $x$ and $y$ if $\left[\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right].$
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Answer
$\begin{array}{l}{\left[\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right]} \end{array}$
$ \Rightarrow\left[\begin{array}{l}2 x+3 x \\ 2 y+4 y\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right] $
$ \Rightarrow\left[\begin{array}{l}5 x \\ 6 y\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right] $
$\Rightarrow 5 x =5 $
$ \Rightarrow x =1$
and
$\Rightarrow 6y = 12$
$\Rightarrow y = 2.$
$ \Rightarrow\left[\begin{array}{l}2 x+3 x \\ 2 y+4 y\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right] $
$ \Rightarrow\left[\begin{array}{l}5 x \\ 6 y\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right] $
$\Rightarrow 5 x =5 $
$ \Rightarrow x =1$
and
$\Rightarrow 6y = 12$
$\Rightarrow y = 2.$
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