Question
Find $x$ and $y$ from the given equations $:\left[\begin{array}{cc}5 & 2 \\ -1 & y-1\end{array}\right]-\left[\begin{array}{cc}1 & x-1 \\ 2 & -3\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right]$
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Answer
$\begin{array}{l}{\left[\begin{array}{cc}5 & 2 \\ -1 & y-1\end{array}\right]-\left[\begin{array}{cc}1 & x-1 \\ 2 & -3\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right]} \end{array} $
$ \Rightarrow\left[\begin{array}{cc}5-1 & 2-x+1 \\ -1-2 & y-1+3\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right] $
$ \Rightarrow\left[\begin{array}{cc}4 & 3-x \\ -3 & y+2\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right]$
Equating the corresponding elements we get
$3 - x = 7$ and $y + 2 = 2$
Thus we get $x = -4$ and $y = 0$
$ \Rightarrow\left[\begin{array}{cc}5-1 & 2-x+1 \\ -1-2 & y-1+3\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right] $
$ \Rightarrow\left[\begin{array}{cc}4 & 3-x \\ -3 & y+2\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ -3 & 2\end{array}\right]$
Equating the corresponding elements we get
$3 - x = 7$ and $y + 2 = 2$
Thus we get $x = -4$ and $y = 0$
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