# Spanning sets and polynomial functions

1. Mar 9, 2009

### ak123456

1. The problem statement, all variables and given/known data

Which o the following are spanning sets for the vector space P2 of polynomial functions of degree 2? (give reasons or your answers)
a.) 2, t^2, t, 2t^2 +3

b.)t+2, t^2 -1

c.) 1,t^2,t^2 -2

2. Relevant equations

3. The attempt at a solution
I'm not entirely sure how to do this but i think i need to show that any vector in P2 can be written as a linear combination of the elements in the set.

P2=a+bt+ct^2 ??
do i need to show a,b,c can form P2 respectively ?

2. Mar 9, 2009

### yyat

If you want to show that, for instance, {2, t^2, t, 2t^2 +3} is a spanning set, then you have to find d,e,f,g (in terms of a,b,c) so that

a+bt+ct^2 = d*(2) + e*(t^2) + f*(t) + g*(2t^2 +3)

because every degree 2 polynomial can be written as a+bt+ct^2 and the RHS is a linear combination of the vectors in the given set.

3. Mar 9, 2009

### ak123456

oh i see ,thanks for your help