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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:
$\begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\\text{x}\end{bmatrix}=0$
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Answer

$\begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\\text{x}\end{bmatrix}=0$
$ \Rightarrow\begin{bmatrix}1+4+1&2+0+0&0+2+2\end{bmatrix}\begin{bmatrix}0\\2\\\text{x}\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}6&2&4\end{bmatrix}\begin{bmatrix}0\\2\\\text{x}\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}0+4+4\text{x}\end{bmatrix}=0$
$\Rightarrow4+4\text{x}=0$
$\Rightarrow4\text{x}=-4$
$\therefore\ \text{x}=\frac{-4}{4}=-1$

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