Find x and y, if [ lll 2 & 0 & 3 ] 3 [ cc 6 & 3 -1 & 2 5 & 4 ]+2 [ cc -4 & -1 1 & 0 -3 & -4 ] = [ ll x & y ]

& Given [ lll 2 & 0 & 3 ] 3 [ cc 6 & 3 -1 & 2 5 & 4 ]+2 [ cc -4 & -1 1 & 0 -3 & -4 ] = [ ll x & y ] & [ lll 2 & 0 & 3 ] [ cc 18 & 9 -3 & 6 15 & 12 ]+ [ cc -8 & -2 2 & 0 -6 & -8 ] = [ ll x & y ] & [ lll 2 & 0 & 3 ] [ cc 10 & 7 -1 & 6 9 & 4 ]= [ ll x & y ] & [ ll 20+27 & 14+12 ]= [ ll x & y ] & [ ll 47 & 26 ]= [ ll x & y ] x=47, y=26 by & definition of equality of matrices.

Find x and y, if [ lll 2 & 0 & 3 ] 3 [ cc 6 & 3 -1 & 2 5 & 4 ]+2 …

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Question

Find $x$ and $y$, if
$
\left[\begin{array}{lll}
2 & 0 & 3
\end{array}\right]\left\{3\left[\begin{array}{cc}
6 & 3 \\
-1 & 2 \\
5 & 4
\end{array}\right]+2\left[\begin{array}{cc}
-4 & -1 \\
1 & 0 \\
-3 & -4
\end{array}\right]\right\}=\left[\begin{array}{ll}
x & y
\end{array}\right]
$

✓

Answer

$
\begin{aligned}
& \text { Given }\left[\begin{array}{lll}
2 & 0 & 3
\end{array}\right]\left\{3\left[\begin{array}{cc}
6 & 3 \\
-1 & 2 \\
5 & 4
\end{array}\right]+2\left[\begin{array}{cc}
-4 & -1 \\
1 & 0 \\
-3 & -4
\end{array}\right]\right\}=\left[\begin{array}{ll}
x & y
\end{array}\right] \\
& \therefore\left[\begin{array}{lll}
2 & 0 & 3
\end{array}\right]\left\{\left[\begin{array}{cc}
18 & 9 \\
-3 & 6 \\
15 & 12
\end{array}\right]+\left[\begin{array}{cc}
-8 & -2 \\
2 & 0 \\
-6 & -8
\end{array}\right]\right\}=\left[\begin{array}{ll}
x & y
\end{array}\right] \\
& \therefore\left[\begin{array}{lll}
2 & 0 & 3
\end{array}\right]\left[\begin{array}{cc}
10 & 7 \\
-1 & 6 \\
9 & 4
\end{array}\right]=\left[\begin{array}{ll}
x & y
\end{array}\right] \\
& \therefore\left[\begin{array}{ll}
20+27 & 14+12
\end{array}\right]=\left[\begin{array}{ll}
x & y
\end{array}\right] \\
& \therefore\left[\begin{array}{ll}
47 & 26
\end{array}\right]=\left[\begin{array}{ll}
x & y
\end{array}\right] \quad \therefore \quad x=47, y=26 \text { by } \\
&
\end{aligned}
$
definition of equality of matrices.