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Homework Help: An Example of a 2-Dimensional Subspace of C[0,1]

  1. Apr 16, 2014 #1


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    1. The problem statement, all variables and given/known data

    Give an example of show that no such example exists.

    A two dimensional subspace of C[0,1]

    2. Relevant equations

    None that I know of.

    3. The attempt at a solution

    I know that C[0,1] is a set of continuous functions but I'm not sure where to go after that.
  2. jcsd
  3. Apr 16, 2014 #2


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    Define what 'two dimensional' means. That should be a clue.
  4. Apr 16, 2014 #3
    Possibly a further clue: how would you find a two-dimensional subspace of ##\mathbb{R}^n##?
  5. Apr 16, 2014 #4


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    Polynomials are continuous functions, aren't they? It should be easy to determine the dimension of a subspace of polynomial functions.
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