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Finding basis for subspace

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data

    find a basis for the subspace R^5 that consists of all the vectors of the form [(b-c), (d-2b), (4d), (c-2d), (6d+2b)]

    2. Relevant equations

    3. The attempt at a solution

    the only solution I can think of is e1, e2, e3, e4, e5... I don't think it's that simple though... would appreciate any input on this question. Thanks!
  2. jcsd
  3. Mar 16, 2009 #2


    Staff: Mentor

    Code (Text):

    a = b - c
    b = -2b   + d
    c =         4d
    d =      c - 2d
    e = 2b     + 6d
    A vector in this subspace is a linear combination of three vectors, which you can pick out of the equations above.
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