Answer
a) $A+B=\left[ \begin{matrix}
3 & 2 & 6 \\
5 & 2 & -8 \\
-2 & 2 & 3 \\
\end{matrix} \right]$
b) $A+B=\left[ \begin{matrix}
3 & 2 & 6 \\
5 & 2 & -8 \\
-2 & 2 & 3 \\
\end{matrix} \right]$
$A-B=\left[ \begin{matrix}
9 & -8 & 4 \\
7 & -2 & 4 \\
-6 & 2 & -5 \\
\end{matrix} \right]$
c) $A+B=\left[ \begin{matrix}
3 & 2 & 6 \\
5 & 2 & -8 \\
-2 & 2 & 3 \\
\end{matrix} \right]$
$\left( -4 \right)A=\left[ \begin{matrix}
-24 & 12 & -20 \\
-24 & 0 & 8 \\
16 & -8 & 4 \\
\end{matrix} \right]$
d) $3A+2B=\left[ \begin{matrix}
12 & 1 & 17 \\
16 & 4 & -18 \\
-8 & 6 & 5 \\
\end{matrix} \right]$
Work Step by Step
(a)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& A+B=\left[ \begin{matrix}
6 & -3 & 5 \\
6 & 0 & -2 \\
-4 & 2 & -1 \\
\end{matrix} \right]+\left[ \begin{matrix}
-3 & 5 & 1 \\
-1 & 2 & -6 \\
2 & 0 & 4 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
3 & 2 & 6 \\
5 & 2 & -8 \\
-2 & 2 & 3 \\
\end{matrix} \right]
\end{align}$
(b)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& A-B=\left[ \begin{matrix}
6 & -3 & 5 \\
6 & 0 & -2 \\
-4 & 2 & -1 \\
\end{matrix} \right]-\left[ \begin{matrix}
-3 & 5 & 1 \\
-1 & 2 & -6 \\
2 & 0 & 4 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
9 & -8 & 4 \\
7 & -2 & 4 \\
-6 & 2 & -5 \\
\end{matrix} \right]
\end{align}$
(c)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& \left( -4 \right)A=\left( -4 \right)\left[ \begin{matrix}
6 & -3 & 5 \\
6 & 0 & -2 \\
-4 & 2 & -1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-24 & 12 & -20 \\
-24 & 0 & 8 \\
16 & -8 & 4 \\
\end{matrix} \right]
\end{align}$
(d)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& 3A+2B=3\left[ \begin{matrix}
6 & -3 & 5 \\
6 & 0 & -2 \\
-4 & 2 & -1 \\
\end{matrix} \right]+2\left[ \begin{matrix}
-3 & 5 & 1 \\
-1 & 2 & -6 \\
2 & 0 & 4 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
18 & -9 & 15 \\
18 & 0 & -6 \\
-12 & 6 & -3 \\
\end{matrix} \right]+\left[ \begin{matrix}
-6 & 10 & 2 \\
-2 & 4 & -12 \\
4 & 0 & 8 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
12 & 1 & 17 \\
16 & 4 & -18 \\
-8 & 6 & 5 \\
\end{matrix} \right]
\end{align}$
