Answer
a. $\left[\begin{array}{lll}
3 & 2 & 6\\
5 & 2 & -8\\
-2 & 2 & 3
\end{array}\right]$
b. $\left[\begin{array}{lll}
9 & -8 & 4\\
7 & -2 & 4\\
-6 & 2 & -5
\end{array}\right]$
c. $\left[\begin{array}{lll}
-24 & 12 & -20\\
-24 & 0 & 8\\
16 & -8 & 4
\end{array}\right]$
d. $\left[\begin{array}{lll}
12 & 1 & 17\\
16 & 4 & -18\\
-8 & 6 & 5
\end{array}\right]$
Work Step by Step
a.
$A+B=[a_{ij}+b_{ij}]$
$=\left[\begin{array}{lll}
6-3 & -3+5 & 5+1\\
6-1 & 0+2 & -2-6\\
-4+2 & 2+0 & -1+4
\end{array}\right]$
$=\left[\begin{array}{lll}
3 & 2 & 6\\
5 & 2 & -8\\
-2 & 2 & 3
\end{array}\right]$
b.
$A-B=[a_{ij}-b_{ij}]$
$=\left[\begin{array}{lll}
6+3 & -3-5 & 5-1\\
6+1 & 0-2 & -2+6\\
-4-2 & 2-0 & -1-4
\end{array}\right]$
$=\left[\begin{array}{lll}
9 & -8 & 4\\
7 & -2 & 4\\
-6 & 2 & -5
\end{array}\right]$
c.
$-4A=\left[-4a_{ij}\right]=\left[\begin{array}{lll}
-24 & 12 & -20\\
-24 & 0 & 8\\
16 & -8 & 4
\end{array}\right]$
d.
$3A+2B=\left[3a_{ij}+2b_{ij}\right]$
$=\left[\begin{array}{lll}
3(6)+2(-3) & 3(-3)+2(5) & 3(5)+2(1)\\
3(6)+2(-1) & 3(0)+2(2) & 3(-2)+2(-6)\\
3(-4)+2(2) & 3(2)+2(0) & 3(-1)+2(4)
\end{array}\right]$
$= \left[\begin{array}{lll}
12 & 1 & 17\\
16 & 4 & -18\\
-8 & 6 & 5
\end{array}\right]$
