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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices5 Marks
Question
Solve the matrix equations:
$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
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Answer

Here,
$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}-2&0-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
$ \Rightarrow\begin{bmatrix}(\text{x}-2)\text{x}-15\end{bmatrix} =0$
$\Rightarrow\text{x}^2-2\text{x}-15=0$
$ \Rightarrow\text{x}^2-5\text{x}+3\text{x}-15=0$
$ \Rightarrow\text{x}(\text{x}-5)+3(\text{x}-5)=0$
$\Rightarrow(\text{x}-5)(\text{x}+3)=0$
$ \Rightarrow\text{x}-5=0\ \text{or}\ \text{x}+3=0$
$ \Rightarrow\text{x}=5\ \text{or}\ \text{x}=-3$
So,
$\text{x}=5\text{ or }-3$

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