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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Find $x$ and $y$ if $\left[\begin{array}{cc}-3 & 2 \\ 0 & -5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right]=\left[\begin{array}{l}5 \\ y\end{array}\right]$
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Answer

$\begin{aligned} & {\left[\begin{array}{cc}-3 & 2 \\ 0 & -5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right]=\left[\begin{array}{l}5 \\ y\end{array}\right]} \end{aligned} $
$ \Rightarrow\left[\begin{array}{cc}-3 x & 4 \\ 0 & -10\end{array}\right]=\left[\begin{array}{c}-5 \\ y\end{array}\right]  $
$ \Rightarrow\left[\begin{array}{cc}-3 x & +4 \\ 0 & -10\end{array}\right]=\left[\begin{array}{c}-5 \\ y\end{array}\right]$
Comparing the corresponding elements
$-3 x+4=-5$
$ \Rightarrow-3 x=-5-4=-9$
$ \therefore x=\frac{-9}{-3}=3$
$ -10=y$
$ \Rightarrow y=-10$
Hence $x=3, y=-10$.

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