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Spaning a set

  • Thread starter Benzoate
  • Start date
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1. Homework Statement
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. Homework 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)}
 

Answers and Replies

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!
 
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If the space you want to span is made up of polynomials, your spanning set should be made of polynomials!
so my spanning set then is : span{(x^3+x^2+1),(x^3-2*x^2+x),(x^3-1)}
 
HallsofIvy
Science Advisor
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Yes, that's fine.
 
HallsofIvy
Science Advisor
Homework Helper
41,736
894
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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