Problem:
Orthogonalize the following vectors:
${\{1,2,3\}, \{-2,-3,-1\}, \{2,-1,3\}}$
Answer:
${\left\{\frac{1}{\sqrt{14}},\sqrt{\frac{2}{7}},\frac{3}{\sqrt{14}}\right\}, \left\{-\frac{17}{5 \sqrt{42}},-2 \sqrt{\frac{2}{21}},\frac{19}{5 \sqrt{42}}\right\}, \left\{\frac{7}{5 \sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{5 \sqrt{3}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/25565.txt'}