Problem:
Orthogonalize the following vectors:
${\{1,-2,1\}, \{2,-3,0\}, \{-2,-2,3\}}$
Answer:
${\left\{\frac{1}{\sqrt{6}},-\sqrt{\frac{2}{3}},\frac{1}{\sqrt{6}}\right\}, \left\{\frac{2}{\sqrt{21}},-\frac{1}{\sqrt{21}},-\frac{4}{\sqrt{21}}\right\}, \left\{-\frac{3}{\sqrt{14}},-\sqrt{\frac{2}{7}},-\frac{1}{\sqrt{14}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/8437.txt'}