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Set of degree 2 polynomials a subspace

  1. Jul 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Which of the subsets of P2 given in exercises 1 through 5 are subspaces of P2? Find a basis for those that are subspaces.

    (P(t)|p(0) = 2)


    2. Relevant equations



    3. The attempt at a solution
    The solution manual says that this subset is not a subspace because it doesn't contain the function f(t) = 0 for all t. I thought the generic element is f(t) = a +bt + ct^2. Why doesn't the element with a = b = c = 0 count as a function f(t) = 0 for all t? I'm stumped.

    Thanks!
     
  2. jcsd
  3. Jul 11, 2010 #2

    Dick

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    Because f(0) isn't equal to 2 with a=0, b=0 and c=0. f(t) isn't in your set.
     
  4. Jul 11, 2010 #3
    Oh, duh. thanks!
     
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