Question
Find $X$ and $Y$ if $X+Y=\left[\begin{array}{ll}7 & 0 \\ 3 & 5\end{array}\right]$ and $X-Y=\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right]$
✓
Answer
$\begin{aligned} & (1)+(2) \Rightarrow 2 X=\left[\begin{array}{cc}10 & 0 \\ 3 & 9\end{array}\right] \\ & \Rightarrow X=\frac{1}{2}\left[\begin{array}{cc}10 & 0 \\ 3 & 9\end{array}\right] \\ & X=\left[\begin{array}{ll}5 & 0 \\ \frac{3}{2} & \frac{9}{2}\end{array}\right] \\ & (1)-(2) \Rightarrow 2 Y=\left[\begin{array}{ll}7 & 0 \\ 3 & 5\end{array}\right]-\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right] \\ & =\left[\begin{array}{ll}4 & 0 \\ 3 & 1\end{array}\right] \\ & \Rightarrow Y=\frac{1}{2}\left[\begin{array}{ll}4 & 0 \\ 3 & 1\end{array}\right] \\ & Y=\left[\begin{array}{ll}2 & 0 \\ \frac{3}{2} & \frac{1}{2}\end{array}\right] \\ & X=\left[\begin{array}{ll}5 & 0 \\ \frac{3}{2} & \frac{9}{2}\end{array}\right] \text { and } Y=\left[\begin{array}{ll}2 & 0 \\ \frac{3}{2} & \frac{1}{2}\end{array}\right]\end{aligned}$
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