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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}1&0\\\text{y}&5\end{bmatrix}+2\begin{bmatrix}\text{x}&0\\1&-2\end{bmatrix}=\text{I},$ where I is 2×2 unit matrix. Find x and y.
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Answer

Given: $\begin{bmatrix}1&0\\\text{y}&5\end{bmatrix}+2\begin{bmatrix}\text{x}&0\\1&-1\end{bmatrix}=\text{I}$
$\Rightarrow\begin{bmatrix}1&0\\\text{y}&5\end{bmatrix}+\begin{bmatrix}2\text{x}&0\\2&-4\end{bmatrix}=\begin{bmatrix}1 &0\\0&1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}1+2\text{x}&0+0\\\text{y}+2&5-4\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}1+2\text{x}&0\\\text{y}+2&1\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$\therefore1+2\text{x}=1$ and $\text{y}+2=0$
$\Rightarrow2\text{x}=1-1$ and $\text{y}=-2$
$\Rightarrow2\text{x}=0$
$\Rightarrow\text{x}=\frac{0}{2}=0$

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