Question

Find the value of $(x\times y)$ if $\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{cc}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right].$

Answer 1

Given $\left[\begin{array}{cc}3& -2\\ 3& 0\\ 2& 4\end{array}\right]\left[\begin{array}{cc}y& y\\ x& x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$
or
$\left[\begin{array}{cc}3y-2x& 3y-2x\\ 3y& 3y\\ 2y+4x& 2y+4x\end{array}\right]=\left[\begin{array}{cc}3& 3\\ 3y& 3y\\ 10& 10\end{array}\right]$

Comparing elements we have
$3y-2x=3$ .......... (1)
$2y+4x=10$ .......... (2)
Solving (1) and (2), we get $x=\frac{3}{2},y=2$

Hence, $xy=3$.