Find X and Y,if X+Y=left[begin{array}{ll}5 &a | vedclass

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Question

(A) Given equations are:
$X + Y = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight]$ --- $(1)$
$X - Y = \left[\begin{array}{cc}3 &

Vedclass · Accepted Answer

$X=\left[\begin{array}{ll}4 & 4 \ 0 & 4\end{array}ight]$,$Y=\left[\begin{array}{rr}1 & -2 \ 0 & 5\end{array}ight]$

Vedclass · Answer

(A) Given equations are:
$X + Y = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight]$ --- $(1)$
$X - Y = \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$ --- $(2)$
Adding equations $(1)$ and $(2)$:
$(X + Y) + (X - Y) = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight] + \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$
$2X = \left[\begin{array}{ll}5+3 & 2+6 \ 0+0 & 9-1\end{array}ight] = \left[\begin{array}{ll}8 & 8 \ 0 & 8\end{array}ight]$
$X = \frac{1}{2} \left[\begin{array}{ll}8 & 8 \ 0 & 8\end{array}ight] = \left[\begin{array}{ll}4 & 4 \ 0 & 4\end{array}ight]$
Subtracting equation $(2)$ from $(1)$:
$(X + Y) - (X - Y) = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight] - \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$
$2Y = \left[\begin{array}{ll}5-3 & 2-6 \ 0-0 & 9-(-1)\end{array}ight] = \left[\begin{array}{ll}2 & -4 \ 0 & 10\end{array}ight]$
$Y = \frac{1}{2} \left[\begin{array}{ll}2 & -4 \ 0 & 10\end{array}ight] = \left[\begin{array}{ll}1 & -2 \ 0 & 5\end{array}ight]$

Find $X$ and $Y$,if $X+Y=\left[\begin{array}{ll}5 & 2 \\ 0 & 9\end{array}\right]$ and $X-Y=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]$.

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