Find the value of y,

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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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