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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Find $x$ and $y$ if $\left[\begin{array}{cc}2 x & x \\ y & 3 y\end{array}\right]\left[\begin{array}{l}3 \\ 2\end{array}\right]=\left[\begin{array}{c}16 \\ 9\end{array}\right]$
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Answer

$
\begin{aligned}
& {\left[\begin{array}{ll}
2 x & x \\
y & 3 y
\end{array}\right]\left[\begin{array}{l}
3 \\
2
\end{array}\right]=\left[\begin{array}{c}
16 \\
9
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{l}
2 x \times 3+x \times 2 \\
y \times 3+3 y \times 2
\end{array}\right]=\left[\begin{array}{c}
16 \\
9
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{l}
6 x+2 x \\
3 y+6 y
\end{array}\right]=\left[\begin{array}{c}
16 \\
9
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{l}
8 x \\
9 y
\end{array}\right]=\left[\begin{array}{c}
16 \\
9
\end{array}\right]
\end{aligned}
$
Comparing, we get
$
\begin{aligned}
& 8 x =16 \\
& \Rightarrow x =\frac{16}{8}=2
\end{aligned}
$
and
$ 9 y=9 $
$ \Rightarrow y=\frac{9}{9}=1$
Here $x =2, y =1$.

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