How to solve this Linear Algebra problem?
I can't figure out how to solve this, since cross product doesn't work in 4 dimensions.
- PopeLv 72 months agoFavorite Answer
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.
- Charles DLv 62 months ago
You have to use the Gram-Schmidt Process for Orthonomalization.
See the Khan Academy Video.
Or google "Gram-Schmidt" to find other explanations. They are about 10 minute videos and probably much better than be done by just typing.
Hope this helps.