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Intersection of sets spanned by polynomials

  1. Oct 11, 2007 #1
    Let s1 be the set spanned by the polynomials: x^3+x+1, x^3-3x^2+x-2, 2x^3-1. Let s2 be the set spanned by the polynomials: x^3-1, x^2+x+1. What is the intersection of s1 and s2?

    I really don't know where to begin, I don't know how to define these sets, s1 and s2. since i don't know what they are it is hard for me to find their intersection.
    Last edited: Oct 11, 2007
  2. jcsd
  3. Oct 11, 2007 #2


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    Not knowing how to start is not great. And and not knowing how to define s1 and s2 is worse. Can't you look that up? If {p1,p2,p3} is a set of polynomials, then the span is the set of all A1*p1+A2*p2+A3*p3 for A1, A2 and A3 real numbers (or complex, or whatever). Similarly for your second set. If you equate the two you should get some linear equations to solve.
  4. Oct 12, 2007 #3

    matt grime

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    Perhaps you're thrown by the fact it's polynomials. If I were to say what is the intersection of the vector subspace of R^4 spanned by

    (1,0,1,1), (1,-3,1,-2), (2,0,0,-1)

    and the vector subspace spanned by

    (1,0,0,-1) and (0,1,1,1)

    wouldn't you have a section in your notes about how to do that?
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