A= [ ll 1 & 2 3 & 4 ] and B= [ ll 6 & 1 1 & 1 ], C= [ cc -2 & -3 … - Vidyadip

Question

$A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $B=\left[\begin{array}{ll}6 & 1 \\ 1 & 1\end{array}\right], C=\left[\begin{array}{cc}-2 & -3 \\ 0 & 1\end{array}\right]$ find each of the following and state if they are equal. $A+C B$

✓

Answer

$
\begin{aligned}
& A + CB \\
& =\left[\begin{array}{ll}
1 & 2 \\
3 & 4
\end{array}\right]+\left[\begin{array}{cc}
-2 & -3 \\
0 & 1
\end{array}\right] \times\left[\begin{array}{ll}
6 & 1 \\
1 & 1
\end{array}\right] \\
& =\left[\begin{array}{ll}
1 & 2 \\
3 & 4
\end{array}\right]+\left[\begin{array}{cc}
-12-3 & -2-3 \\
0+1 & 0+1
\end{array}\right] \\
& =\left[\begin{array}{ll}
1 & 2 \\
3 & 4
\end{array}\right]+\left[\begin{array}{cc}
-15 & -5 \\
1 & 1
\end{array}\right] \\
& =\left[\begin{array}{cc}
1-15 & 2-5 \\
3+1 & 4+1
\end{array}\right] \\
& =\left[\begin{array}{cc}
-14 & -3 \\
4 & 5
\end{array}\right]
\end{aligned}
$
We can say that $C A+B \neq A+C B$.

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