Question
$\left[\begin{array}{ll}1 & 2 \\ 3 & 3\end{array}\right]\left[\begin{array}{ll}x & 0 \\ 0 & y\end{array}\right]=\left[\begin{array}{ll}x & 0 \\ 9 & 0\end{array}\right]$ find the values of $x$ and $y$
✓
Answer
Given
$
\begin{aligned}
& {\left[\begin{array}{ll}
1 & 2 \\
3 & 3
\end{array}\right]\left[\begin{array}{ll}
x & 0 \\
0 & y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{cc}
x+0 & 0 \\
3 x+2 y \\
3 x+0 & 0+3 y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
x & 2 y \\
3 x & 3 y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements
$
\begin{aligned}
& 2 y=0 \\
& \Rightarrow y=0 \\
& 3 x=9 \\
& \Rightarrow x=3
\end{aligned}
$
Hence $x =3, y =0$.
$
\begin{aligned}
& {\left[\begin{array}{ll}
1 & 2 \\
3 & 3
\end{array}\right]\left[\begin{array}{ll}
x & 0 \\
0 & y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{cc}
x+0 & 0 \\
3 x+2 y \\
3 x+0 & 0+3 y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
x & 2 y \\
3 x & 3 y
\end{array}\right]=\left[\begin{array}{ll}
x & 0 \\
9 & 0
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements
$
\begin{aligned}
& 2 y=0 \\
& \Rightarrow y=0 \\
& 3 x=9 \\
& \Rightarrow x=3
\end{aligned}
$
Hence $x =3, y =0$.
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