Given A= [ cc 1 & 1 -2 & 0 ] and B= [ cc 2 & -1 1 & 1 ] Solve for… - Vidyadip

Question

Given $A=\left[\begin{array}{cc}1 & 1 \\ -2 & 0\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$ Solve for matrix $X: 3A - 2X = X - 2B$

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Answer

$3A - 2X = X - 2B$
$3A + 2B = X + 2X$
$3X = 3A + 2B$
$\begin{array}{l}3 X=3\left[\begin{array}{cc}1 & 1 \\ -2 & 0\end{array}\right]+2\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]\end{array} $
$ 3 X=\left[\begin{array}{cc}7 & 1 \\ -4 & 2\end{array}\right] $
$ X=\left[\begin{array}{cc}\frac{7}{3} & \frac{1}{3} \\ -\frac{4}{3} & \frac{2}{3}\end{array}\right]$

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