If $\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{ll}2 & 1 \\ 4 & 3\end{array}\right]\left[\begin{array}{c}1 \\ -2\end{array}\right]$, then write the value of $(x, y)$.
$\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{ll}2 & 1 \\ 4 & 3\end{array}\right]\left[\begin{array}{c}1 \\ -2\end{array}\right]$
$\Rightarrow\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{c}2-2 \\ 4-6\end{array}\right]$
$\Rightarrow\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{c}0 \\ -2\end{array}\right]$
Corresponding elements of equal matrices are equal.
$\therefore x+y=0 \quad$ and $\quad x-y=-2$
$\Rightarrow x=-y \quad$ and $\quad-y-y=-2$
$\Rightarrow x=-y \quad$ and $\quad y=1$
$\Rightarrow x=-1 \quad$ and $\quad y=1$
Hence, $(x, y)=(-1,1)$
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