Question

Find x and y if $\left[\begin{array}{cc}2x& x\\ y& 3y\end{array}\right]\left[\begin{array}{c}3\\ 2\end{array}\right]=\left[\begin{array}{c}16\\ 9\end{array}\right]$

Answer 1

$\left(\begin{array}{cc}2x& x\\ y& 3y\end{array}\right)\left(\begin{array}{c}3\\ 2\end{array}\right)=\left(\begin{array}{c}16\\ 9\end{array}\right)]$

Multiplying the rows of the first matrix and the first column of the second matrix we get the following matrix as

$\left(\begin{array}{c}6x+2x\\ 3y+6y\end{array}\right)=\left(\begin{array}{c}16\\ 9\end{array}\right)$

$\left(\begin{array}{c}8x\\ 9y\end{array}\right)=\left(\begin{array}{c}16\\ 9\end{array}\right)$

$8x=16$

$⟹x=2$

$9y=9$

$⟹y=1$

$sox=2,y=1$