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Orthogonalizing a basis by gram schmidt process

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data

    (a.) Find an orthonormal basis of R^4 spanned by {1,1,1,1},{1,0,0,1}, and {0,1,0,1}.
    (b.) Use the inner product to express {2,2,2,2} as a linear combination of the basis vectors. Do not solve the equations.

    2. Relevant equations

    gram schmidt orthogonalization and then normalizing

    3. The attempt at a solution

    (a.) I used gram schmidt orthogonalization and then normalized to get:

    1/2{1,1,1,1}, 1/2{1,-1,-1,1}, 1/2{-1,1,-1,1}

    (b.) I'm not sure how to do this, any help would be appreciated.
     
  2. jcsd
  3. Nov 6, 2012 #2

    LCKurtz

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    So you want$$
    (2,2,2,2) = \frac {c_1}2 (1,1,1,1)+\frac {c_2}2 (1,-1,-1,1)+\frac {c_3}2 (-1,1,-1,1)$$What happens if you take the inner product of both sides of that with one of your basis vectors?
     
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