Hey guys, here is a linear algebra problem that I need to do, help would be much appreciated.

Consider the functions p1 : R R, p2 : R R, p3 : R R, defined by

p1(x) = 1 + x + 2x^{2}, p2(x) = 7 + 8x + 13x^{2}, p3(x) = −3 − x − 7x^{2}.

Let B = {p1, p2, p3} and let W = span(B).

Show that B is a basis for W.

Find dim(W).

Show that W = P2.

Thanks for your help!