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
    Favorite 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.

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    • 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.

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  • 4 weeks 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.

    • jay4 weeks agoReport

      thank you

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