Question:
If $\left[\begin{array}{cc}x & x-y \\ 2 x+y & 7\end{array}\right]=\left[\begin{array}{ll}3 & 1 \\ 8 & 7\end{array}\right]$, then find the value of $y$.
Solution:
We have, $\left[\begin{array}{cc}x & x-y \\ 2 x+y & 7\end{array}\right]=\left[\begin{array}{ll}3 & 1 \\ 8 & 7\end{array}\right]$
The corresponding elements of two equal matrices are equal.
$\therefore x=3$
$x-y=1 \quad \ldots(1)$
Putting the value of $x$ in eq. (1)
$3-y=1$
$\Rightarrow 3-1=y$
$\therefore y=2$
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