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Vector Space

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Is the set of all polynomials with positive coefficients a vector space?

    It's not.

    But after going through the vector space conditions I don't see how it can't be.
     
  2. jcsd
  3. Apr 15, 2013 #2

    jedishrfu

    Staff: Mentor

    what are the inverse elements of the space?
     
  4. Apr 15, 2013 #3

    mfb

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    2016 Award

    Staff: Mentor

    If you show your work, it is easier to find your error.
    Oh, and you have to specify the field for the vector space (probably R).

    Edit: Or use the direct hint given above ;).
     
  5. Apr 15, 2013 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    One of the properties that a vector space must have is that it is "closed under scalar multiplication". That is, the product of any real number a, and vector v, av is also a number. v= x+ 1 is a "polynomial with positive coefficients" and a= -1 is a number. What is av?
     
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