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Homework Help: Why is the following not a subspace?

  1. Oct 28, 2012 #1
    I attached the problem, the solutions say its not a subspace.

    To be a subspace it must satisfy 3 conditions
    1) 0 is in S
    2) if U and V are in S, then U+V must be in S
    3) if V is in S, then fV is in S for some scalar f.

    0 is in S

    U+V is in S because if U and V have elements that are negative for y, then the addition or those are still less than 0.

    fV isn't in S because if the scalar was a negative number then y would be greater than 0. Is this why it's not a subspace?

    Attached Files:

  2. jcsd
  3. Oct 28, 2012 #2


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    That should be "for any scalar f"
    Yes, but I'd prefer to be a little more precise. You should say "fV is not always in S", and it won't generate an exception if y happens to be zero. Give a specific example V, f, for which fV would not be in S.
  4. Oct 28, 2012 #3
    Exactly.It is also not closed under summation.
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