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Linear algebra - basis of subspace

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a basis of the subspace of R4 that consists of all vectors perpendicular to both

    (1
    0
    5
    2)

    and

    (0
    1
    5
    5)

    ^ those are vectors.


    2. Relevant equations



    3. The attempt at a solution

    I understand that a basis needs to be linearly independent and that it needs to span the vector space, but I am thrown off by the fact that the basis needs to consist of vectors perpendicular to those vectors above.
     
  2. jcsd
  3. Nov 12, 2009 #2
    do you know about orthogonal projections? or perhaps the gram-schmidt process? seems like the perfect time to use it. dont know if wikipedia links are allowed to be posted here, but here is a link to gram schmidt in case you havent read about it. the process itself might seem tedious but is very simple.

    http://en.wikipedia.org/wiki/Gram–Schmidt_process

    hope this helps.

    cj.
     
  4. Nov 12, 2009 #3

    Mark44

    Staff: Mentor

    Another approach is to Let u = (u1, u2, u3, u4) be a vector in R4.

    Since u is perpendicular to both of your given vectors, the dot product of u with each of the given vectors should be 0. That will give you two equations in four unknowns. These equations can be used to find a basis for your subspace.
     
    Last edited: Nov 12, 2009
  5. Nov 12, 2009 #4
    thanks! i got it :)
     
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