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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right],$ find the values of $\mathrm{x}$ and $\mathrm{y}$.
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Answer

Given: $x\left[ {\begin{array}{*{20}{c}} 2 \\ 3 \end{array}} \right] + y\left[ {\begin{array}{*{20}{c}} { - 1} \\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {10} \\ 5 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} {2x} \\ {3x} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} { - y} \\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {10} \\ 5 \end{array}} \right]$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} {2x - y} \\ {3x + y} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {10} \\ 5 \end{array}} \right]$
Equating corresponding entries, we have
$2x - y = 10 ……….(i) $ and
$3x + y = 5 ……….(ii)$
Adding eq. $(i)$ and $(ii),$
we have $5x = 15$
$\Rightarrow x = 3$
Putting $x = 3$ in eq. $(ii),$
$9 + y = 5$
$\Rightarrow y = -4$

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