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Vector Spaces & Subspaces, Linear Algebra

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Let V be a vector space and U a subspace of V . For a given x ∈ V , define T=
    {x + u | u ∈ U }. Show that T is a subspace of V if and only if x ∈ U .

    2. Relevant equations
    Subspace Test:
    1: The 0 vector of V is included in T.
    2: T is closed under vector addition
    3: T is closed under scalar multiplication

    3. The attempt at a solution
    I do not know how to show this...
  2. jcsd
  3. Jan 25, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    You're not trying very hard. Start with the forward direction. Show T is a subspace if x is in U. Try showing in this case T=U.
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