Question:
Find the value of $y$, if $\left[\begin{array}{ll}x-y & 2 \\ x & 5\end{array}\right]=\left[\begin{array}{ll}2 & 2 \\ 3 & 5\end{array}\right]$
Solution:
Given : $\left[\begin{array}{cc}x-y & 2 \\ x & 5\end{array}\right]=\left[\begin{array}{ll}2 & 2 \\ 3 & 5\end{array}\right]$
The corresponding elements of two equal matrices are equal.
$\therefore x-y=2 \quad \ldots(1)$
and $x=3$
Putting the value of $x$ in eq. (1)
$3-y=2$
$\Rightarrow 3-2=y$
$\therefore y=1$
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