Problem:
Add the two matrices
$\left(
\begin{array}{ccc}
 -7 & -\frac{20}{7} & -\frac{1}{7} \\
 -\frac{32}{7} & -\frac{48}{7} & \frac{33}{7} \\
\end{array}
\right)$ and
$\left(
\begin{array}{ccc}
 -\frac{65}{7} & -\frac{17}{7} & \frac{40}{7} \\
 -\frac{68}{7} & \frac{54}{7} & \frac{66}{7} \\
\end{array}
\right)$
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Simplify the following}: \\
 \left(
\begin{array}{ccc}
 -7 & -\frac{20}{7} & -\frac{1}{7} \\
 -\frac{32}{7} & -\frac{48}{7} & \frac{33}{7} \\
\end{array}
\right)+\left(
\begin{array}{ccc}
 -\frac{65}{7} & -\frac{17}{7} & \frac{40}{7} \\
 -\frac{68}{7} & \frac{54}{7} & \frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \left(
\begin{array}{ccc}
 -7 & -\frac{20}{7} & -\frac{1}{7} \\
 -\frac{32}{7} & -\frac{48}{7} & \frac{33}{7} \\
\end{array}
\right)+\left(
\begin{array}{ccc}
 -\frac{65}{7} & -\frac{17}{7} & \frac{40}{7} \\
 -\frac{68}{7} & \frac{54}{7} & \frac{66}{7} \\
\end{array}
\right)=\left(
\begin{array}{ccc}
 -7-\frac{65}{7} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right): \\
 \left(
\begin{array}{ccc}
 -7-\frac{65}{7} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Put }-7-\frac{65}{7} \text{over }\text{the }\text{common }\text{denominator }7. -7-\frac{65}{7} \text{= }\frac{7 (-7)}{7}-\frac{65}{7}: \\
 \left(
\begin{array}{ccc}
 \fbox{$\frac{7 (-7)}{7}-\frac{65}{7}$} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 7 (-7) \text{= }-49: \\
 \left(
\begin{array}{ccc}
 \frac{\fbox{$-49$}}{7}-\frac{65}{7} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -\frac{49}{7}-\frac{65}{7} \text{= }\frac{-49-65}{7}: \\
 \left(
\begin{array}{ccc}
 \fbox{$\frac{-49-65}{7}$} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -49-65=-(49+65): \\
 \left(
\begin{array}{ccc}
 \frac{\fbox{$-(49+65)$}}{7} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
\hline
 \text{} & 1 & \text{} \\
\hline
 \text{} & 6 & 5 \\
 + & 4 & 9 \\
 1 & 1 & 4 \\
\end{array}
 \\
\end{array}
: \\
 \left(
\begin{array}{ccc}
 \frac{-\fbox{$114$}}{7} & -\frac{20}{7}-\frac{17}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -\frac{20}{7}-\frac{17}{7} \text{= }\frac{-20-17}{7}: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & \fbox{$\frac{-20-17}{7}$} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -20-17=-(20+17): \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & \frac{\fbox{$-(20+17)$}}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
\hline
 \text{} & 2 & 0 \\
\hline
 + & 1 & 7 \\
 \text{} & 3 & 7 \\
\end{array}
 \\
\end{array}
: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & \frac{-\fbox{$37$}}{7} & -\frac{1}{7}+\frac{40}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -\frac{1}{7}+\frac{40}{7} \text{= }\frac{-1+40}{7}: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \fbox{$\frac{-1+40}{7}$} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -1+40=39: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{\fbox{$39$}}{7} \\
 -\frac{32}{7}-\frac{68}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -\frac{32}{7}-\frac{68}{7} \text{= }\frac{-32-68}{7}: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 \fbox{$\frac{-32-68}{7}$} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -32-68=-(32+68): \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 \frac{\fbox{$-(32+68)$}}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
\hline
 \text{} & 1 & \text{} \\
\hline
 \text{} & 6 & 8 \\
 + & 3 & 2 \\
 1 & 0 & 0 \\
\end{array}
 \\
\end{array}
: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 \frac{-\fbox{$100$}}{7} & -\frac{48}{7}+\frac{54}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -\frac{48}{7}+\frac{54}{7} \text{= }\frac{-48+54}{7}: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 -\frac{100}{7} & \fbox{$\frac{-48+54}{7}$} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -48+54=6: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 -\frac{100}{7} & \frac{\fbox{$6$}}{7} & \frac{33}{7}+\frac{66}{7} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 \frac{33}{7}+\frac{66}{7} \text{= }\frac{33+66}{7}: \\
 \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 -\frac{100}{7} & \frac{6}{7} & \fbox{$\frac{33+66}{7}$} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
\hline
 \text{} & 6 & 6 \\
\hline
 + & 3 & 3 \\
 \text{} & 9 & 9 \\
\end{array}
 \\
\end{array}
: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \left(
\begin{array}{ccc}
 -\frac{114}{7} & -\frac{37}{7} & \frac{39}{7} \\
 -\frac{100}{7} & \frac{6}{7} & \frac{\fbox{$99$}}{7} \\
\end{array}
\right) \\
\end{array}
$} \\
\end{array}
 \\
\end{array}
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/add_w_steps/3867.txt'}