# Spaning a set

1. Mar 31, 2008

### Benzoate

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. Mar 31, 2008

### quasar987

If the space you want to span is made up of polynomials, your spanning set should be made of polynomials!

3. Mar 31, 2008

### Benzoate

so my spanning set then is : span{(x^3+x^2+1),(x^3-2*x^2+x),(x^3-1)}

4. Mar 31, 2008

### HallsofIvy

Staff Emeritus
Yes, that's fine.

5. Mar 31, 2008

### HallsofIvy

Staff Emeritus
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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