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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices5 Marks
Question
Solve the matrix equations:
$\begin{bmatrix}2\text{x}&3\end{bmatrix}\begin{bmatrix}1&2\\-3&0\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
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Answer

$\begin{bmatrix}2\text{x}&3\end{bmatrix}\begin{bmatrix}1&2\\-3&0\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}2\text{x}-9&4\text{x}\end{bmatrix}\begin{bmatrix}\text{x}\\8\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}(2\text{x}-9)+32\text{x}\end{bmatrix}=0$
$ \Rightarrow\begin{bmatrix}2\text{x}^2-9\text{x}+32\text{x}\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}2\text{x}^2+23\text{x}\end{bmatrix}=0$
$\Rightarrow2\text{x}^2+23\text{x}=0$
$\Rightarrow\text{x}(2\text{x}+23)=0$
$\Rightarrow\text{x}=0\ \text{or }\text{x}=-\frac{23}{2}$
$\therefore\ \text{x}=0\ \text{or }\text{x}=-\frac{23}{2}$

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