For the inner product spaces V (over F) and linear transformations g: V->F, find a vector y such that g(x)=<x,y> for all x in V.
(1) V=R^3, g(a_1,a_2,a_3)=a_1-2a_2+4a_3
(2) V=P2(R) with <f,h>= integral 0 to1 f(t)h(t)dt, g(f)=f(0)+f'(1)
ps: i'm trying my best with the latex, but for some reason when i use it the page gets all distorted.
Thanks! But for "umber 2 I went and found an orthonormal basis to the inner product using gram schmidt and got {1, 2sqt(3)(x-1/2), 6sqt(5)(x^2-x+1/6}. Then I went on like number one and I'm stuck. I'm not coming anywhere close to the answer given in the back of the book. I hope someone can give me some direction.
Just in case, the answer given is: 210x^2-204x+33