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