jay asked in Science & MathematicsMathematics · 4 weeks ago

# 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.

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• Pope
Lv 7
4 weeks ago

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.

• Pope
Lv 7
4 weeks agoReport

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.

• 4 weeks ago

You have to use the Gram-Schmidt Process for Orthonomalization.