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Homework Help: Not a Vector Space

  1. Jun 2, 2014 #1
    1. The problem statement, all variables and given/known data

    For each of the following sets, either verify (as in Example 1) that it is a vector space, or show which requirements are not satisfied. If it is a vector space, find a basis and the dimension of the space.

    6. Polynomials of degree ≤ 6 with a3 = 3.

    2. Relevant equations


    3. The attempt at a solution

    I put that it was a vector space with the basis of {1,x,x^2,3*x^3,x^4,x^5,x^6} and dimension of 7. I am not sure why it fails to be a vector space.

  2. jcsd
  3. Jun 2, 2014 #2


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    What happens if you add two members of the given set, or if you multiply a member by a scalar?
  4. Jun 2, 2014 #3
    I think there is a closure problem because one would not be able to get rid of the 3*x^3 by playing with coefficients.

    I will have to think about it a little more.

  5. Jun 2, 2014 #4


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