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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices5 Marks
Question
$=\begin{bmatrix}1&1&\text{x}\end{bmatrix}\begin{bmatrix}1&0&2\\0&2&1\\2&1&0\end{bmatrix}\begin{bmatrix}1\\1\\1\end{bmatrix}=0,$ find x.
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Answer

Given: $=\begin{bmatrix}1&1&\text{x}\end{bmatrix}\begin{bmatrix}1&0&2\\0&2&1\\2&1&0\end{bmatrix}\begin{bmatrix}1\\1\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}1+0+2\text{x}&0+2+\text{x}&2+1+0\end{bmatrix}\begin{bmatrix}1\\1\\1\end{bmatrix}=0$
$\begin{bmatrix}1+2\text{x}&2+\text{x}&3\end{bmatrix}\begin{bmatrix}1\\1\\1\end{bmatrix}=0$
$\Rightarrow[1+2\text{x}+2+\text{x}+3]=0$
$\Rightarrow6+3\text{x}=0$
$\Rightarrow3\text{x}=-6$
$\Rightarrow\text{x}=\frac{-6}{3}$
$\therefore\ \text{x}=-2$

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