Problem:
Add the two matrices
$\left(
\begin{array}{ccc}
 2 & 1 & 6 \\
 8 & 4 & -3 \\
 9 & -5 & -1 \\
\end{array}
\right)$ and
$\left(
\begin{array}{ccc}
 -10 & -9 & 8 \\
 -2 & 8 & -4 \\
 2 & -8 & -10 \\
\end{array}
\right)$
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Simplify the following}: \\
 \left(
\begin{array}{ccc}
 2 & 1 & 6 \\
 8 & 4 & -3 \\
 9 & -5 & -1 \\
\end{array}
\right)+\left(
\begin{array}{ccc}
 -10 & -9 & 8 \\
 -2 & 8 & -4 \\
 2 & -8 & -10 \\
\end{array}
\right) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \left(
\begin{array}{ccc}
 2 & 1 & 6 \\
 8 & 4 & -3 \\
 9 & -5 & -1 \\
\end{array}
\right)+\left(
\begin{array}{ccc}
 -10 & -9 & 8 \\
 -2 & 8 & -4 \\
 2 & -8 & -10 \\
\end{array}
\right)=\left(
\begin{array}{ccc}
 2-10 & 1-9 & 6+8 \\
 8-2 & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right): \\
 \left(
\begin{array}{ccc}
 2-10 & 1-9 & 6+8 \\
 8-2 & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 2-10=-8: \\
 \left(
\begin{array}{ccc}
 \fbox{$-8$} & 1-9 & 6+8 \\
 8-2 & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 1-9=-8: \\
 \left(
\begin{array}{ccc}
 -8 & \fbox{$-8$} & 6+8 \\
 8-2 & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 6+8=14: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & \fbox{$14$} \\
 8-2 & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 8-2=6: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 \fbox{$6$} & 4+8 & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 4+8=12: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & \fbox{$12$} & -3-4 \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -3-4=-(3+4): \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & \fbox{$-(3+4)$} \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 3+4=7: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -\fbox{$7$} \\
 9+2 & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 9+2=11: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -7 \\
 \fbox{$11$} & -5-8 & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -5-8=-(5+8): \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -7 \\
 11 & \fbox{$-(5+8)$} & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 5+8=13: \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -7 \\
 11 & -\fbox{$13$} & -1-10 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 -1-10=-(1+10): \\
 \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -7 \\
 11 & -13 & \fbox{$-(1+10)$} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 1+10=11: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \left(
\begin{array}{ccc}
 -8 & -8 & 14 \\
 6 & 12 & -7 \\
 11 & -13 & -\fbox{$11$} \\
\end{array}
\right) \\
\end{array}
$} \\
\end{array}
 \\
\end{array}
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/add_w_steps/4996.txt'}