Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    0 \in W

    a \in W, b \in W \rightarrow a + b \in W

    a \in \mathbb{K}, v \in W \rightarrow a.v \in W

    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


    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    also your argument is correct.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Question in test
  1. Independence test (Replies: 4)

  2. Semiprime test (Replies: 17)

  3. Test for Primes (Replies: 5)

  4. Subring Test (Replies: 4)