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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Find $x$ and $y$ if $\left[\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right]$
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Answer

$\begin{array}{l}{\left[\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right]}\end{array} $
$ {\left[\begin{array}{l}2 x+3 x \\ 2 y+4 y\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right]} $
$ {\left[\begin{array}{l}5 x \\ 6 y\end{array}\right] =\left[\begin{array}{c}5 \\ 12\end{array}\right]}$
Comparing the corresponding elements we get
$5 x=5 \Rightarrow x=1$
$6 y=12\Rightarrow x=1$
$6 y=12\Rightarrow y=2$

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