# 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.

### 2 Answers

- 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.

https://www.khanacademy.org/math/linear-algebra/al...

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.

thank you

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All four components matter. There was nothing special about the first two until I had substituted arbitrary constants for the last two. I could have chosen any two of the four components for that substitution.