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Homework Help: Vector bases and functions

  1. Oct 27, 2008 #1
    Hi

    How can I work out which subset is a subspace and which one isnt on this problem:

    Fq ([0,1]) be vector space of all functions [0,1] -> Q with addition and scalar multiplication defined in usual way.

    Let U < Fq ([0,1]) be the subset consisting of all functions f s.t. f(0) >= f(1) and let
    V < Fq([0,1]) be subset consist of all functions f such that f(0) = f(1).

    ===

    And lastly if C2 is a complex vector space consisting of pairs (z1 and z2) of complex numbers whats the 3 different bases for (Complex numbers base 2)?
     
  2. jcsd
  3. Oct 27, 2008 #2

    HallsofIvy

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    Science Advisor

    To prove that "U is a subspace of V" you must only prove that, for any u, v in U, au+bv is int U which is equivalent to proving "if u and v are in U, then u+v is in U" and "if u is in U and a is a scalar, then au is int U'.

    I have no idea what you mean by this. There exit an infinite number of bases for any vector space. Nor do I understand what you mean by "Complex numbers base 2". Do you mean "modulo 2"?
     
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