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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices5 Marks
Question
If $\text{A}=\begin{bmatrix}2&-2\\4&2\\-5&1\end{bmatrix},\text{ B}=\begin{bmatrix}8&0\\4&-2\\3&6\end{bmatrix},$ find matrix X such that 2A + 3X = 5B.
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Answer

Given, $2\text{A}+3\text{X}=5\text{B}$
$\Rightarrow2\begin{bmatrix}2&-2\\4&2\\-5&1\end{bmatrix}+3\text{X}=5\begin{bmatrix}8&0\\4&-2\\3&6\end{bmatrix}$
$\Rightarrow\begin{bmatrix}4&-4\\8&4\\-10&2\end{bmatrix}+3\text{X}=\begin{bmatrix}40&0\\20&-10\\15&30\end{bmatrix}$
$\Rightarrow3\text{X}=\begin{bmatrix}40&0\\20&-10\\15&30\end{bmatrix}-\begin{bmatrix}4&-4\\8&4\\-10&2\end{bmatrix}$
$\Rightarrow3\text{X}=\begin{bmatrix}40-4&0+4\\20-8&-10-4\\15+10&30-2\end{bmatrix}$
$\Rightarrow3\text{X}=\begin{bmatrix}36&4\\12&-14\\25&28\end{bmatrix}$
$\Rightarrow\text{X}=\frac{1}{3}\begin{bmatrix}36&4\\12&-14\\25&28\end{bmatrix}$
$\Rightarrow\text{X}=\begin{bmatrix}12&\frac{4}{3}\\4&\frac{-14}{3}\\\frac{25}{3}&\frac{28}{3}\end{bmatrix}$

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