Find X, if Y = [ ll 3 & 2 1 & 4 ] and 2 X+Y= [ rr 1 & 0 -3 & 2 ] - Vidyadip

Question

Find X, if Y = $\left[\begin{array}{ll} {3} & {2} \\ {1} & {4} \end{array}\right] \text { and } 2 \mathrm{X}+\mathrm{Y}=\left[\begin{array}{rr} {1} & {0} \\ {-3} & {2} \end{array}\right]$

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Answer

2X + Y = $\left[\begin{array}{cc} {1} & {0} \\ {-3} & {2} \end{array}\right]$
$\Rightarrow 2 \mathrm{X}+\left[\begin{array}{ll} {3} & {2} \\ {1} & {4} \end{array}\right]=\left[\begin{array}{cc} {1} & {0} \\ {-3} & {2} \end{array}\right]$
$\Rightarrow 2 \mathrm{X}=\left[\begin{array}{cc} {1} & {0} \\ {-3} & {2} \end{array}\right]-\left[\begin{array}{cc} {3} & {2} \\ {1} & {4} \end{array}\right]$
$\Rightarrow 2 \mathrm{X}=\left[\begin{array}{cc} {1-3} & {0-2} \\ {-3-1} & {2-4} \end{array}\right]$
$\Rightarrow 2 \mathrm{X}=\left[\begin{array}{cc} {-2} & {-2} \\ {-4} & {-2} \end{array}\right]$
$\Rightarrow X=\frac{1}{2}\left[\begin{array}{ll} {-2} & {-2} \\ {-4} & {-2} \end{array}\right]$
$\Rightarrow X=\left[\begin{array}{cc} {-1} & {-1} \\ {-2} & {-1} \end{array}\right]$

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