Problem:
Orthogonalize the following vectors:
${\{0,1,-3\}, \{-3,-2,1\}, \{-1,-1,-1\}}$
Answer:
${\left\{0,\frac{1}{\sqrt{10}},-\frac{3}{\sqrt{10}}\right\}, \left\{-3 \sqrt{\frac{2}{23}},-\frac{3}{\sqrt{46}},-\frac{1}{\sqrt{46}}\right\}, \left\{\sqrt{\frac{5}{23}},-\frac{9}{\sqrt{115}},-\frac{3}{\sqrt{115}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/10115.txt'}