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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
Find $x$ and $y$, if $2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$.
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Answer

Given: $2\left[ {\begin{array}{*{20}{c}} 1&3 \\ 0&x \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} y&0 \\ 1&2 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} 2&6 \\ 0&{2x} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} y&0 \\ 1&2 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} {2 + y}&6 \\ 1&{2x + x} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5&6 \\ 1&8 \end{array}} \right]$
Equating corresponding entries, we have
2 + y = 5 and 2x + 2 = 8
$\Rightarrow$ y = 5 - 2 and 2(x + 1) = 8
$\Rightarrow$ y = 3 and x + 1 = 4
$\Rightarrow$ y = 3 and x = 3

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