If $\left[\begin{array}{ll}1 & 0 \\ y & 5\end{array}\right]+2\left[\begin{array}{rr}x & 0 \\ 1 & -2\end{array}\right]=l$, where $l$ is $2 \times 2$ unit matrix. Find $x$ and $y$.
Given : $\left[\begin{array}{ll}1 & 0 \\ y & 5\end{array}\right]+2\left[\begin{array}{cc}x & 0 \\ 1 & -2\end{array}\right]=I$
$\Rightarrow\left[\begin{array}{cc}1 & 0 \\ y & 5\end{array}\right]+\left[\begin{array}{cc}2 x & 0 \\ 2 & -4\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}1+2 x & 0+0 \\ y+2 & 5-4\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}1+2 x & 0 \\ y+2 & 1\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\therefore 1+2 x=1$ and $y+2=0$
$\Rightarrow 2 x=1-1$ and $y=-2$
$\Rightarrow 2 x=0$
$\Rightarrow x=\frac{0}{2}=0$
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