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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices2 Marks
Question
If $2\begin{bmatrix}3&4\\5&\text{x}\end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1\end{bmatrix}=\begin{bmatrix}7&0\\10&5\end{bmatrix},$ find x and y.
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Answer

Given: $2\begin{bmatrix}3&4\\5&\text{x}\end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1\end{bmatrix}=\begin{bmatrix}7&0\\10&5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}6&8\\10&2\text{x}\end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1\end{bmatrix}=\begin{bmatrix}7&0\\10&5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}6+1&8+\text{y}\\10+0&2\text{x}+1\end{bmatrix}=\begin{bmatrix}7&0\\10&5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}7&8+\text{y}\\10&2\text{x}+1 \end{bmatrix}\begin{bmatrix}7&0\\10&5\end{bmatrix}$
$\therefore\ 8+\text{y}=0$
$\Rightarrow\text{y}=-8$
Also,
$2\text{x}+1=5$
$\Rightarrow2\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{2}=2$
$\therefore\ \text{x}=2$ and $\text{y}=-8$

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