Yahoo Answers: Answers and Comments for How to solve this Linear Algebra problem? [Mathematics]
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From jay
enUS
Tue, 28 Jan 2020 01:06:18 +0000
3
Yahoo Answers: Answers and Comments for How to solve this Linear Algebra problem? [Mathematics]
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From Pope: The conditions for vector x leave it open to i...
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Tue, 28 Jan 2020 02:45:28 +0000
The conditions for vector x leave it open to infinitely many solutions. Give the third and fourth components arbitrary values 1 and 0, and solve for the first two.
x = <a, b, 1, 0>
u·x = v·x = 0
2a + 3b = b + 2 = 0
b = 2
2a + 3(2) = 0
a = 3
x = <3, 2, 1, 0>
For vector y use a similar procedure, employing different arbitrary values for two components. Do not simply change the third component; that would only steer you toward a scalar multiple.

From Charles D: You have to use the GramSchmidt Process for O...
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Tue, 28 Jan 2020 02:17:29 +0000
You have to use the GramSchmidt Process for Orthonomalization.
See the Khan Academy Video.
https://www.khanacademy.org/math/linearalgebra/alternatebases/orthonormalbasis/v/linearalgebrathegramschmidtprocess
Or google "GramSchmidt" to find other explanations. They are about 10 minute videos and probably much better than be done by just typing.
Hope this helps.