Answer
a) $A+B=\left[ \begin{matrix}
10 & 0 & 0 \\
\end{matrix} \right]$
b) $A-B=\left[ \begin{matrix}
2 & 4 & -6 \\
\end{matrix} \right]$
c) $\left( -4 \right)A=\left[ \begin{matrix}
-24 & -8 & 12 \\
\end{matrix} \right]$
d) $3A+2B=\left[ \begin{matrix}
26 & 2 & -3 \\
\end{matrix} \right]$
Work Step by Step
(a)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& A+B=\left[ \begin{matrix}
6 & 2 & -3 \\
\end{matrix} \right]+\left[ \begin{matrix}
4 & -2 & 3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
10 & 0 & 0 \\
\end{matrix} \right]
\end{align}$
(b)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& A-B=\left[ \begin{matrix}
6 & 2 & -3 \\
\end{matrix} \right]-\left[ \begin{matrix}
4 & -2 & 3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
2 & 4 & -6 \\
\end{matrix} \right]
\end{align}$
(c)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& \left( -4 \right)A=\left( -4 \right)\left[ \begin{matrix}
6 & 2 & -3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-24 & -8 & 12 \\
\end{matrix} \right]
\end{align}$
(d)
Perform the addition of the matrices $A$ and $B$ as below:
$\begin{align}
& 3A+2B=3\left[ \begin{matrix}
6 & 2 & -3 \\
\end{matrix} \right]+2\left[ \begin{matrix}
4 & -2 & 3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
18 & 6 & -9 \\
\end{matrix} \right]+\left[ \begin{matrix}
8 & -4 & 6 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
26 & 2 & -3 \\
\end{matrix} \right]
\end{align}$
