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Another subspace prove

  1. Mar 4, 2009 #1
    there are two W1 and W2 of F^3 space
    dim(W1)=1
    dim(W2)=2

    prove or desprove that:

    [tex]W1\cap W2[/tex]={0} is the vector space
    ??

    there could be a case where W2 includes W1 then there intersection is not the 0 space
    correct??
     
  2. jcsd
  3. Mar 4, 2009 #2
    If there are no other constraints on the problem then yeah.

    Take a plane going through the origin and a line contained on that plane in R^3.

    That seems like a silly problem though. Do you know anything else like

    W1+W2 = W3 (direct sum?)
     
  4. Mar 4, 2009 #3
    can you give an actual example
    ??
     
  5. Mar 4, 2009 #4
    I am just saying your counterexample (or one like it) works as long as there are no other restrictions on the problem.

    If we require that W1+W2 = F^3, then it is true, because one space cannot contain the other.
     
  6. Mar 4, 2009 #5
    if W2 include W1
    and we have another subspace W3
    which
    dim W3=1
    then dimW2+dimW3=3

    what is the problem in that??
     
  7. Mar 4, 2009 #6
    Nothing, that's tenable.
     
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