Problem:
Orthogonalize the following vectors:
${\{3,-3,0\}, \{0,-3,-1\}, \{2,-1,-3\}}$
Answer:
${\left\{\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}},0\right\}, \left\{-\frac{3}{\sqrt{22}},-\frac{3}{\sqrt{22}},-\sqrt{\frac{2}{11}}\right\}, \left\{\frac{1}{\sqrt{11}},\frac{1}{\sqrt{11}},-\frac{3}{\sqrt{11}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/1508.txt'}