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Spaning a set

  1. Mar 31, 2008 #1
    1. The problem statement, all variables and given/known data
    Find a spanning set for the vector space consisting of all polynomials of the form:
    (a+b+c)x^3+(a-2b)x^2+bx-c+a


    2. Relevant equations



    3. The attempt at a solution

    a(1,0,1,1)+b(0,1,-2,1)+c(-1,0,0,1). So my spanning set is : {(1,0,1,1),(0,1,-2,1),(-1,0,0,1)}
     
  2. jcsd
  3. Mar 31, 2008 #2

    quasar987

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    If the space you want to span is made up of polynomials, your spanning set should be made of polynomials!
     
  4. Mar 31, 2008 #3
    so my spanning set then is : span{(x^3+x^2+1),(x^3-2*x^2+x),(x^3-1)}
     
  5. Mar 31, 2008 #4

    HallsofIvy

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    Yes, that's fine.
     
  6. Mar 31, 2008 #5

    HallsofIvy

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    Yes, that's fine.
    Another way of doing exactly the same thing:
    You are given that the set of polynomials is all polynomials of the form (a+b+c)x^3+(a-2b)x^2+bx-c+a

    Let a= 1, b= c= 0 and that is x^3+ x^2+ 1.
    Let b= 1, a= c= 0 and that is x^3+ x^2+ x
    Let c= 1, a= b= 0 and that is x^3- 1, exactly what you have.
     
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