Problem:
Orthogonalize the following vectors:
${\{-3,3,-2\}, \{0,1,-3\}, \{1,-2,-2\}}$
Answer:
${\left\{-\frac{3}{\sqrt{22}},\frac{3}{\sqrt{22}},-\sqrt{\frac{2}{11}}\right\}, \left\{\frac{27}{\sqrt{3058}},-\frac{5}{\sqrt{3058}},-24 \sqrt{\frac{2}{1529}}\right\}, \left\{-\frac{7}{\sqrt{139}},-\frac{9}{\sqrt{139}},-\frac{3}{\sqrt{139}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/48457.txt'}