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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices5 Marks
Question
Solve the matrix equations:
$\begin{bmatrix}\text{x}&-5&-1\end{bmatrix}\begin{bmatrix}1&0&2\\0&2&1\\2&0&3\end{bmatrix}\begin{bmatrix}\text{x}\\4\\1\end{bmatrix}=0$
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Answer

$\begin{bmatrix}\text{x}&-5&-1\end{bmatrix}\begin{bmatrix}1&0&2\\0&2&1\\2&0&3\end{bmatrix}\begin{bmatrix}\text{x}\\4\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}-0-2&0-10-0&2\text{x}-5-3\end{bmatrix}\begin{bmatrix}\text{x}\\4\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}-2&-10&2\text{x}-8\end{bmatrix}\begin{bmatrix}\text{x}\\4\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}\text{x}^2-2\text{x}-40+2\text{x}-8\end{bmatrix}=0$
$ \Rightarrow\text{x}^2-48=0$
$\Rightarrow\text{x}^2=48$
$ \Rightarrow\text{x}=\pm\sqrt{48}$

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