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Really basic linear algebra: subspaces of F[a,b]

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Determine which of the following sets of functions are subsets of F[a,b]

    a) All functions f in F[a,b] for which f(a) = 0
    b) All functions f in F[a,b] for which f(a) = 1


    3. The attempt at a solution

    Ok so I am just learning about vector subspaces. After reading the text multiple times, I am still at a lost. Can someone please explain to me in plain English what these evil math people want from me?

    Thanks guys for your much appreciated help :smile:
     
  2. jcsd
  3. Feb 15, 2010 #2

    vela

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    What's F[a,b] defined as? I assume it's some set of functions defined on the interval [a,b], but what particular properties must these functions have?
     
  4. Feb 15, 2010 #3
    Thanks for your reply! Unfortunately F wasn't given any particular properties
     
  5. Feb 15, 2010 #4

    Hurkyl

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    What is F[a,b] defined as?


    P.S. did you mean "subset of F[a,b]" or did you mean "subspace of F[a,b]"?
     
  6. Feb 16, 2010 #5
    oops sorry about that, I meant "subspace of F[a,b]"

    F is the matrix with vectors a and b? :|
     
  7. Feb 16, 2010 #6

    Mark44

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    That doesn't make any sense. Instead of guessing, please tell us what F[a, b] means relative to this problem. It should say in the problem itself.
     
  8. Feb 16, 2010 #7

    vela

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    OK, the first thing you need to do is go figure out what the notation "F[a,b]" means. Don't just make wild guesses. It should be explained in your textbook or notes somewhere.
     
  9. Feb 16, 2010 #8
    You have to think about the basic closed under addition and closed under multiplication properties, to see if a) or b) satisfy them.
    For example, would adding f(a)=0 and say g(a)=0 still be in this subspace?
    What about for f(a)+g(a) = 1 + 1?
    That should give you a clear hint.
     
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