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Subspaces of R2 and R3

  1. Mar 4, 2008 #1
    So I'm considering dimensions of real vector spaces.

    I found myself thinking about the following:

    So for the vector space R2 there are the following possible subspaces:
    1. {0}
    2. R2
    3. All the lines through the origin.

    Then I considered R3.

    For the vector space R3 there are the following subspaces:
    1. {0}
    2. R3
    3. All lines through the origin.
    4. All planes through the origin.

    Although I "know" (4.) to be true... I can't figure out a mathematical why or a solid way of proving it.

    Any hints?
  2. jcsd
  3. Mar 4, 2008 #2
    what is the equation of a plane through the origin? you should show that the set consisting of all points that lie on this plane(ie, satisfy this equation once you get it) is a subspace of R^3
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