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Linear Algebra - Affine subsets, proving M = U + a is unique

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let M be an affine subset of V.

    We then prove that if 0 ∈ M then M is a subspace.

    There exists a subspace U of V and a ∈ V such that
    M = U + a. (1)

    Show that the subspace U in (1) is uniquely determined by M and describe the extent to which a is determined by M.

    2. Relevant equations

    An affine subset of V is a non-empty subset M of V with the property that λx+(1−λ)y ∈ M whenever x,y ∈ M and λ ∈ R.

    3. The attempt at a solution

    Not sure.
  2. jcsd
  3. Mar 13, 2012 #2


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