Problem:
Orthogonalize the following vectors:
${\left\{-\frac{5}{3},\frac{5}{3},-2\right\}, \left\{0,-\frac{1}{3},-1\right\}, \left\{\frac{8}{3},-\frac{2}{3},\frac{5}{3}\right\}}$
Answer:
${\left\{-\frac{5}{\sqrt{86}},\frac{5}{\sqrt{86}},-3 \sqrt{\frac{2}{43}}\right\}, \left\{\frac{65}{\sqrt{59426}},-\frac{151}{\sqrt{59426}},-90 \sqrt{\frac{2}{29713}}\right\}, \left\{\frac{21}{\sqrt{691}},\frac{15}{\sqrt{691}},-\frac{5}{\sqrt{691}}\right\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/13388.txt'}