Find X, if
Question:

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

Solution:

$2 X+Y=\left[\begin{array}{rr}1 & 0 \\ -3 & 2\end{array}\right]$

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

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

$\Rightarrow 2 X=\left[\begin{array}{ll}-2 & -2 \\ -4 & -2\end{array}\right]$

$\therefore X=\frac{1}{2}\left[\begin{array}{ll}-2 & -2 \\ -4 & -2\end{array}\right]=\left[\begin{array}{ll}-1 & -1 \\ -2 & -1\end{array}\right]$

 

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