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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES5 Marks
Question
Find non-zero values of x satisfying the matrix equation:$\text{x}\begin{bmatrix}2\text{x}&2\\3&\text{x}\end{bmatrix}+2\begin{bmatrix}8&5\text{x}\\4&4\text{x}\end{bmatrix}=2\begin{bmatrix}(\text{x}^2+8)&24(10)&6\text{x}\end{bmatrix}$
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Answer

Consider, $\text{x}\begin{bmatrix}2\text{x}&2\\3&\text{x}\end{bmatrix}+2\begin{bmatrix}8&5\text{x}\\4&4\text{x}\end{bmatrix}=2\begin{bmatrix}(\text{x}^2+8)&24(10)&6\text{x}\end{bmatrix}$$\Rightarrow\ \begin{bmatrix}2\text{x}^2&2\text{x}\\3\text{x}&\text{x}^2\end{bmatrix}+\begin{bmatrix}16&10\text{x}\\8&8\text{x}\end{bmatrix}=\begin{bmatrix}2\text{x}^2+16&48\\20&12\text{x}\end{bmatrix}$
$\Rightarrow\ \begin{bmatrix}2\text{x}^2+16&2\text{x}+10\text{x}\\3\text{x}+8&\text{x}^2+8\end{bmatrix}=\begin{bmatrix}2\text{x}^2+16&48\\20&12\text{x}\end{bmatrix}$
$\Rightarrow\ 2\text{x}+10\text{x}=48$
$\Rightarrow\ 12\text{x}=48$
$\Rightarrow\ \text{x}=\frac{48}{12}=4$

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