Problem:
Find the $\ell_2$ norm of the following vector:
$\left(
\begin{array}{c}
 -\frac{29}{7} \\
 \frac{38}{7} \\
 \frac{41}{7} \\
 -\frac{47}{7} \\
 \frac{54}{7} \\
 \frac{30}{7} \\
 -\frac{61}{7} \\
\end{array}
\right)$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the norm of the vector }\, \left(-\frac{29}{7},\frac{38}{7},\frac{41}{7},-\frac{47}{7},\frac{54}{7},\frac{30}{7},-\frac{61}{7}\right)\, : \\
 \left\| \, \left(-\frac{29}{7},\frac{38}{7},\frac{41}{7},-\frac{47}{7},\frac{54}{7},\frac{30}{7},-\frac{61}{7}\right)\, \right\|  \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{The }\text{formula }\text{for }\text{the }\text{7-dimensional }\text{Euclidean }\text{norm }\text{comes }\text{from }\text{the }\text{7-dimensional }\text{Pythagorean }\text{theorem}: \\
 \left\| \, \left(v_1,v_2,v_3,v_4,v_5,v_6,v_7\right)\, \right\| =\sqrt{v_1^2+v_2^2+v_3^2+v_4^2+v_5^2+v_6^2+v_7^2} \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Substitute }\, \left(-\frac{29}{7},\frac{38}{7},\frac{41}{7},-\frac{47}{7},\frac{54}{7},\frac{30}{7},-\frac{61}{7}\right)\,  \text{into }\text{the }\text{formula}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \left\| \, \left(-\frac{29}{7},\frac{38}{7},\frac{41}{7},-\frac{47}{7},\frac{54}{7},\frac{30}{7},-\frac{61}{7}\right)\, \right\| =\sqrt{\left(\frac{-29}{7}\right)^2+\left(\frac{38}{7}\right)^2+\left(\frac{41}{7}\right)^2+\left(\frac{-47}{7}\right)^2+\left(\frac{54}{7}\right)^2+\left(\frac{30}{7}\right)^2+\left(\frac{-61}{7}\right)^2}=\frac{4 \sqrt{857}}{7} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/lp_norm_w_steps/100.txt'}