Hi guy's I was wondering if someone could give me some tips in proving that:

{1,t,t^2} is a basis for real polynomials P^2

I know I need to show 2 things,

1 That the vectors are linearly indepenedent and
2 They generate all vectors in P^2

Suppose we have real numbers a b c

I need to show that


a(1) + b(t) + c(t^2) = 0


but not sure how to prove this



To show that it generates polynomials in P^2 can I just choose a polynomial of P^2 and show the linear combination?

eg

To generate 5+2t +6t^2

we let e_1 = 1 e_2 = t and e_3 = t^2

5+2t +6t^2 = 5*(e_1)+ 2*(e_2) + 6*(e_3)

regards
Brendan