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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
Solve for $x$ and $y : \left[\begin{array}{ll}2 & 5 \\ 5 & 2\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}-7 \\ 14\end{array}\right]$
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Answer

$\begin{array}{l}{\left[\begin{array}{ll}2 & 5 \\ 5 & 2\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}-7 \\ 14\end{array}\right]} \end{array} $
$ {\left[\begin{array}{l}2 x+5 y \\ 5 x+2 y\end{array}\right]=\left[\begin{array}{l}-7 \\ 14\end{array}\right]}$
Comparing the corresponding elements, we get
$2x + 5y = -7 ....(1)$
$5x + 2y = 14 ....(2)$
Multiplying $(1)$ and $2$ and $(2)$ with $5$ we get
$4x + 10y = -14...(3)$
$25x + 10y = 70 ....(4)$
Substracting $(3)$ from $(4),$ we get
$21x = 84 $
$\Rightarrow x = 4$
From $(2), 2y = 14 - 5x $
$= 14 - 20 $
$= -6 $
$\Rightarrow y = -3$

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