Problem:
Orthogonalize the following vectors:
${\left\{-\frac{6}{5},\frac{2}{5},-\frac{9}{5}\right\}, \left\{\frac{2}{5},-\frac{3}{5},2\right\}, \left\{\frac{3}{5},\frac{3}{5},\frac{13}{5}\right\}}$
Answer:
${\left\{-\frac{6}{11},\frac{2}{11},-\frac{9}{11}\right\}, \left\{-\frac{58}{11 \sqrt{41}},-\frac{21}{11 \sqrt{41}},\frac{34}{11 \sqrt{41}}\right\}, \left\{-\frac{1}{\sqrt{41}},\frac{6}{\sqrt{41}},\frac{2}{\sqrt{41}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/10123.txt'}