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Homework Help: Subspace of vector space

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine whether or not the given set is a subspace of the indicated vector space:
    Functions f such that [integral from a to b]f(x)dx = 0; C[a,b]
    (not sure how to do the coding for integrals)

    2. Relevant equations
    to be a subspace it must follow these axioms:
    (i) if x and y are in W, then x + y is in W.
    (ii) if x is in W and k is any scalar, then kx is in W.

    3. The attempt at a solution

    im having trouble understanding this. what exactly is C[a,b]?
  2. jcsd
  3. Sep 26, 2009 #2


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    Homework Helper

    could it be the set of all continuous functions defined on [a,b]?

    is there any more to the question?
  4. Sep 27, 2009 #3
    0 + 0 = 0

    c0 = 0 where c is an arbitrary constant.

    Use properties of the integral.
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