Find X if Y= 3&2 1&4 and 2X+Y= 1&0 -3&2 - Vidyadip

Question

Find $\text{X if Y}=\begin{bmatrix}3&2\\1&4\end{bmatrix}$ and $2\text{X}+\text{Y}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}$

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Answer

$2\text{X}+\text{Y}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}$
$\Rightarrow2\text{X}+\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}$
$\Rightarrow2\text{X}+\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}$
$\Rightarrow2\text{X}=\frac{1}{2}\begin{bmatrix}1&0\\-3&2\end{bmatrix}-\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1-3&0-2\\-3-1&2-4\end{bmatrix}$
$\Rightarrow2\text{X}=\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}$
$\therefore\ \text{X}=\frac{1}{2}=\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}=\begin{bmatrix}-1&-1\\-2&-1\end{bmatrix}$

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