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Question in test

  1. Dec 27, 2004 #1
    Hi all,

    this question was in a test the previous year:

    Decide, whether this statement is right or not (in accord with the content of the lecture). Justify your decision:

    Let V be a vector space and U its subspace. Then, in some cases V \ U could be the subspace of V, but generally it doesn't have to be a subspace of V

    I think that V \ U can't be a subspace, because each subspace must fit this conditions:

    [tex]
    0 \in W
    [/tex]

    [tex]
    a \in W, b \in W \rightarrow a + b \in W
    [/tex]

    [tex]
    a \in \mathbb{K}, v \in W \rightarrow a.v \in W
    [/tex]

    So, if U is subspace, it contains 0. So, V \ U doesn't contain 0 => it isn't a subspace.

    Is this a right conclusion?

    Thank you.
     
  2. jcsd
  3. Dec 27, 2004 #2
    It's correct.
     
  4. Dec 28, 2004 #3
    Just for the safety's sake - you mean my conclusion is correct or the statement is correct? :smile:
     
  5. Dec 28, 2004 #4
    Oh, didn't see that ambiguity. ;) I mean that your conclusion was correct.
     
  6. Dec 28, 2004 #5

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    also your argument is correct.
     
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