Problem:
Compute the trace of
$\left(
\begin{array}{ccc}
 \frac{37}{5} & \frac{11}{5} & 2 \\
 \frac{17}{5} & -\frac{47}{5} & \frac{9}{5} \\
 -\frac{37}{5} & 1 & -\frac{21}{5} \\
\end{array}
\right)$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the trace of the matrix:} \\
 \left(
\begin{array}{ccc}
 \frac{37}{5} & \frac{11}{5} & 2 \\
 \frac{17}{5} & -\frac{47}{5} & \frac{9}{5} \\
 -\frac{37}{5} & 1 & -\frac{21}{5} \\
\end{array}
\right) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{Locate }\text{the }\text{elements }\text{on }\text{the }\text{main }\text{diagonal}: \\
 \left(
\begin{array}{ccc}
 \frac{37}{5} & \frac{11}{5} & 2 \\
 \frac{17}{5} & -\frac{47}{5} & \frac{9}{5} \\
 -\frac{37}{5} & 1 & -\frac{21}{5} \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Write }\text{out }\text{the }\text{sum }\text{of }\text{the }\text{elements }\text{on }\text{the }\text{main }\text{diagonal}: \\
 \frac{37}{5}\, \text{+$\, $}-\frac{47}{5}\, \text{+$\, $}-\frac{21}{5} \\
\end{array}
 \\
 
\begin{array}{l}
 \frac{37}{5}-\frac{47}{5}-\frac{21}{5} \text{= }\frac{37-47-21}{5}: \\
 \frac{37-47-21}{5} \\
\end{array}
 \\
 
\begin{array}{l}
 37-47-21=37-(47+21): \\
 \frac{\fbox{$37-(47+21)$}}{5} \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
\hline
 \text{} & 4 & 7 \\
\hline
 + & 2 & 1 \\
 \text{} & 6 & 8 \\
\end{array}
 \\
\end{array}
: \\
 \frac{37-\fbox{$68$}}{5} \\
\end{array}
 \\
 
\begin{array}{l}
 37-68 \text{= }-(68-37): \\
 \frac{\fbox{$-(68-37)$}}{5} \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{c}
 
\begin{array}{ccc}
 \text{} & 6 & 8 \\
 - & 3 & 7 \\
\hline
 \text{} & 3 & 1 \\
\end{array}
 \\
\end{array}
: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \frac{-\fbox{$31$}}{5} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/trace_w_steps/4835.txt'}