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Help Needed for Vector Space Proof

  1. Mar 18, 2008 #1

    Well i hv just started vector spaces and well am finding difficulty in proving this hoffman and kunze problem could some 1 help me :(

    Question : W1 and W2 be sub-spaces of vector space V such that set-theoritic union of W1 and W2 is also a Subspace . Proove that one of the subspace Wi is contained in other ?

    Thank You
  2. jcsd
  3. Mar 18, 2008 #2
    so you have that W_1, W_2 are subspaces

    you need to show that if W_1 U W_2 is a subspace then W_1 is contained in W_2, or W_2 is contained in W_1

    the contrapositive is easier to prove, you should show that
    if W_1 is not contained in W_2 and W_2 is not contained in W_1, then W_1 U W_2 is not a subspace
    hint: W_1 U W_2 won't be closed under addition, show this and you are done
  4. Mar 18, 2008 #3


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    i.e. use contradiction.
  5. Mar 19, 2008 #4
    Hey thanx was able to do the proof by proving the contradicton
  6. Mar 19, 2008 #5
    Where is Applied maths

    Please I wanna know if there is a forum that is talking about applied maths ..

    If there. u can send me an e-mail at>>> ( ahmedtomyus@yahoo.com )
  7. Mar 21, 2008 #6


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    What do you mean by "applied maths"?
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