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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Find $x$ and $y$ if $\left[\begin{array}{cc}x & 0 \\ -3 & 1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 0 & y\end{array}\right]=\left[\begin{array}{cc}2 & 2 \\ -3 & -2\end{array}\right]$
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Answer

$\begin{array}{l}{\left[\begin{array}{cc}x & 0 \\ -3 & 1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 0 & y\end{array}\right]=\left[\begin{array}{cc}2 & 2 \\ -3 & -2\end{array}\right]}\end{array}  $
$ {\left[\begin{array}{cc}x+0 & x+0 \\ -3+0 & -3+y\end{array}\right]=\left[\begin{array}{cc}2 & 2 \\ -3 & -2\end{array}\right]}  $
$ {\left[\begin{array}{cc}x & x \\ -3 & -3+y\end{array}\right]=\left[\begin{array}{cc}2 & 2 \\ -3 & -2\end{array}\right]}$
Comparing the corresponding elements we get
$x = 2$
$-3+y=-2 $
$\Rightarrow y=1$

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