Answer
a. $\left[\begin{array}{lll}
5 & -2 & 7\\
-4 & 3 & 1
\end{array}\right]$
b. $\left[\begin{array}{lll}
1 & 4 & -5\\
2 & 1 & 9
\end{array}\right]$
c. $\left[\begin{array}{lll}
-12 & -4 & -4\\
4 & -8 & -20
\end{array}\right]$
d. $\left[\begin{array}{lll}
13 & -3 & 15\\
-9 & 8 & 7
\end{array}\right]$
Work Step by Step
a.
$A+B=[a_{ij}+b_{ij}]$
$A+B=\left[\begin{array}{lll}
3+2 & 1+(-3) & 1+6\\
-1+(-3) & 2+1 & 5+(-4)
\end{array}\right]$
$=\left[\begin{array}{lll}
5 & -2 & 7\\
-4 & 3 & 1
\end{array}\right]$
b.
$A-B=[a_{ij}-b_{ij}]$
$A-B=\left[\begin{array}{lll}
3-2 & 1-(-3) & 1-6\\
-1-(-3) & 2-1 & 5-(-4)
\end{array}\right]$
$=\left[\begin{array}{lll}
1 & 4 & -5\\
2 & 1 & 9
\end{array}\right]$
c.
$-4A=\left[-4a_{ij}\right]$
$-4A=\left[\begin{array}{lll}
-12 & -4 & -4\\
4 & -8 & -20
\end{array}\right]$
d.
$3A+2B=\left[3a_{ij}+2b_{ij}\right]$
$=\left[\begin{array}{lll}
3\times 3+2\times 2 & 3\times 1+2(-3) & 3\times 1+2\times 6\\
3(-1)+2(-3) & 3\times 2+2\times 1 & 3\times 5+2(-4)
\end{array}\right]$
$=\left[\begin{array}{lll}
13 & -3 & 15\\
-9 & 8 & 7
\end{array}\right]$
