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Math Help - finding an orthonormal basis

  1. #1
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    finding an orthonormal basis

    I'm trying to find an orthonormal basis for the subspace \mathbf{R}^3 consisint of all vectors (a,b,c) such that a+b+2c=0. Can I use Gram Schmidt? I don't know what to do about the constraint?
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  2. #2
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    Quote Originally Posted by superdude View Post
    I'm trying to find an orthonormal basis for the subspace \mathbf{R}^3 consisint of all vectors (a,b,c) such that a+b+2c=0. Can I use Gram Schmidt? I don't know what to do about the constraint?
    Well, before you can use "Gram-Schmidt" to find an orthonormal basis, you have to have a basis!

    From a+ b+ 2c, you can get a= -b- 2c so (a, b, c)= (-b- 2c, b, c)= b(-1, 1, 0)+ c(-2, 0, 1). Do you see the two basis vectors? Use Gram-Schmidt on them.
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  3. #3
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    (-1, 1, 0) and (-2, 0, 1) thanks!
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