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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Find $x$ and $y$ if $x\left[\begin{array}{c}-1 \\ 2\end{array}\right]-4\left[\begin{array}{c}-2 \\ y\end{array}\right]=\left[\begin{array}{c}7 \\ -8\end{array}\right]$
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Answer

$\begin{array}{l}x\left[\begin{array}{c}-1 \\ 2\end{array}\right]-4\left[\begin{array}{c}-2 \\ y\end{array}\right]=\left[\begin{array}{c}7   -8\end{array}\right] \end{array} $
$ {\left[\begin{array}{c}-x \\ 2 x\end{array}\right]-\left[\begin{array}{c}-8 \\ 4 y\end{array}\right]=\left[\begin{array}{c}7 \\ -8\end{array}\right]}  $
$ {\left[\begin{array}{c}-x+8 \\ 2 x-4 y\end{array}\right]=\left[\begin{array}{c}7 \\ -8\end{array}\right]}$
Comparing corresponding the elements we get
$-x + 8 = 7$ and $2x - 4y = -8$
Simplifying we get
$x=1$ and $y=\frac{5}{2}=2.5$

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