Question

Find $x+y$ if $\left[\begin{array}{cc}x& 3x\\ y& 4y\end{array}\right]$ $\left[\begin{array}{c}2\\ 1\end{array}\right]$ $=\left[\begin{array}{c}5\\ 12\end{array}\right]$.

Answer 1

Given:

$\left[\begin{array}{cc}x& 3x\\ y& 4y\end{array}\right]\left[\begin{array}{c}2\\ 1\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}2x+3x\\ 2y+4y\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}5x\\ 6y\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]$

$\Rightarrow x=1,y=2$
$\therefore x+y=3$