Find the value of x and y, when
i. $\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{l}8 \\ 4\end{array}\right]$
If $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}e & f \\ g & h\end{array}\right]$
Then a=e, b=f, c=g, d=h
Given $\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{l}8 \\ 4\end{array}\right]$
So, $x+y=8$ and $x-y=4$
Adding these two gives $2 x=12$
$\Rightarrow x=6$
$y=2$
Conclusion : $x=6$ and $y=2$
ii. $\left[\begin{array}{cc}2 \mathrm{x}+5 & 7 \\ 0 & 3 \mathrm{y}-7\end{array}\right]=\left[\begin{array}{cc}\mathrm{x}-3 & 7 \\ 0 & -5\end{array}\right]$
Given, $\left[\begin{array}{cc}2 x+5 & 7 \\ 0 & 3 y-7\end{array}\right]=\left[\begin{array}{cc}x-3 & 7 \\ 0 & -5\end{array}\right]$
So, $2 x+5=x-3$ and $3 y-7=-5$
$\Rightarrow 3 y=2 \Rightarrow y=\frac{2}{3}$
$\Rightarrow 2 x+5=x-3 \Rightarrow x=-8$
Conclusion : $x=-8$ and $y=\frac{2}{3}$
iii. $2\left[\begin{array}{cc}\mathrm{x} & 5 \\ 7 & \mathrm{y}-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]$
$2\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]$
$\left[\begin{array}{cc}2 x+3 & 6 \\ 15 & 2 y-4\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]$
$2 x+3=7 \Rightarrow x=2$
$2 y-4=14 \Rightarrow y=9$
Conclusion : $x=2$ and $y=9$
(Given answer is wrong)
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