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Homework Help: Finding basis probelm

  1. Dec 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Let S be the form of (a, b,c ,d )in R4, given a not equal to 0. Find the basis that is subset of S.


    2. Relevant equations



    3. The attempt at a solution
    I got a(1,0,0,0), b(0,1,0,0), c(0,0,1,0), d(0,0,0,1) as basis. a not = 0
    But i wasn't sure what the significances of a not = to 0 means

    Any help would be appreciated.
    Thanks in advance.
     
  2. jcsd
  3. Dec 11, 2009 #2

    LCKurtz

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    It means find four elements of R4 that are linearly independent and all of whose first components are non-zero. That would comprise such a basis.
     
  4. Dec 12, 2009 #3

    HallsofIvy

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    However, the set of all (a, b, c, d) in R4 such that [itex]a\ne 0[/itex] is NOT a subspace and so does NOT have a basis. Are you sure you have read the problem correctly?
     
  5. Dec 12, 2009 #4

    LCKurtz

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    I'm thinking the OP may have the problem stated correctly since he/she calls S a set. They just seek a basis for R4 choosing only from that set.
     
  6. Dec 13, 2009 #5

    HallsofIvy

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    Ah! You are right. I misread it. The problem is NOT to find a basis for S but to find a basis for R4 such that the first component of each basis vector is not 0.
    I would be inclined to take the "standard" basis and change the first component of each to a simple non-zero number. Then check to see if they are still independent.
     
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