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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
Find X if $\text {Y} = \begin{bmatrix}3&2\\1&4\end{bmatrix} \text{and}\ \text{2X + Y} = \begin{bmatrix}1&0\\-3&2\end{bmatrix}.$
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Answer

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

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