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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 $y=7$

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