Question:
If $\left[\begin{array}{rr}x+3 & 4 \\ y-4 & x+y\end{array}\right]=\left[\begin{array}{ll}5 & 4 \\ 3 & 9\end{array}\right]$, find $x$ and $y$
Solution:
The corresponding elements of two equal matrices are equal.
Given : $\left[\begin{array}{cc}x+3 & 4 \\ y-4 & x+y\end{array}\right]=\left[\begin{array}{ll}5 & 4 \\ 3 & 9\end{array}\right]$
$x+3=5$ and $y-4=3$
$\Rightarrow x=5-3$ and $y=3+4$
$\Rightarrow x=2$ and $y=7$
$\therefore x=2$ and $y=7$