Answer
a) $A+B=\left[ \begin{matrix}
8 & 0 & -4 \\
14 & 0 & 6 \\
-1 & 0 & 0 \\
\end{matrix} \right]$
b) $A-B=\left[ \begin{matrix}
-4 & -20 & 0 \\
14 & 24 & 14 \\
9 & -4 & 4 \\
\end{matrix} \right]$
c) $\left( -4 \right)A=\left[ \begin{matrix}
-8 & 40 & 8 \\
-56 & -48 & -40 \\
-16 & 8 & -8 \\
\end{matrix} \right]$
d) $3A+2B=\left[ \begin{matrix}
18 & -10 & -10 \\
42 & 12 & 22 \\
2 & -2 & 2 \\
\end{matrix} \right]$
Work Step by Step
(a)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& A+B=\left[ \begin{matrix}
2 & -10 & -2 \\
14 & 12 & 10 \\
4 & -2 & 2 \\
\end{matrix} \right]+\left[ \begin{matrix}
6 & 10 & -2 \\
0 & -12 & -4 \\
-5 & 2 & -2 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
8 & 0 & -4 \\
14 & 0 & 6 \\
-1 & 0 & 0 \\
\end{matrix} \right]
\end{align}$
(b)
Perform the addition of the matrices $A$ and $B$ as follows:
$\begin{align}
& A-B=\left[ \begin{matrix}
2 & -10 & -2 \\
14 & 12 & 10 \\
4 & -2 & 2 \\
\end{matrix} \right]-\left[ \begin{matrix}
6 & 10 & -2 \\
0 & -12 & -4 \\
-5 & 2 & -2 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-4 & -20 & 0 \\
14 & 24 & 14 \\
9 & -4 & 4 \\
\end{matrix} \right]
\end{align}$
(c)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& \left( -4 \right)A=\left( -4 \right)\left[ \begin{matrix}
2 & -10 & -2 \\
14 & 12 & 10 \\
4 & -2 & 2 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-8 & 40 & 8 \\
-56 & -48 & -40 \\
-16 & 8 & -8 \\
\end{matrix} \right]
\end{align}$
(d)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& 3A+2B=3\left[ \begin{matrix}
2 & -10 & -2 \\
14 & 12 & 10 \\
4 & -2 & 2 \\
\end{matrix} \right]+2\left[ \begin{matrix}
6 & 10 & -2 \\
0 & -12 & -4 \\
-5 & 2 & -2 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
6 & -30 & -6 \\
42 & 36 & 30 \\
12 & -6 & 6 \\
\end{matrix} \right]+\left[ \begin{matrix}
12 & 20 & -4 \\
0 & -24 & -8 \\
-10 & 4 & -4 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
18 & -10 & -10 \\
42 & 12 & 22 \\
2 & -2 & 2 \\
\end{matrix} \right]
\end{align}$
