linear algebra: Let V = P1(R), f1, f2 in V* be defined by...

[x3non25]

hi i'm new to this site and was wondering if i can get some help:

Let V=P[sub:frx0y6b8]1[/sub:frx0y6b8](R) and let f[sub:frx0y6b8]1[/sub:frx0y6b8], f[sub:frx0y6b8]2[/sub:frx0y6b8] be in the set V[sup:frx0y6b8]*[/sup:frx0y6b8] be defined by
f[sub:frx0y6b8]1[/sub:frx0y6b8](p) = int[0,1] p(t) dt, f[sub:frx0y6b8]2[/sub:frx0y6b8](p) = int[0,2] p(t) dt, p in the set V

prove that (beta)[sup:frx0y6b8]*[/sup:frx0y6b8] = {f[sub:frx0y6b8]1[/sub:frx0y6b8],f[sub:frx0y6b8]2[/sub:frx0y6b8]} is a basis for V[sup:frx0y6b8]*[/sup:frx0y6b8], and find a basis (beta) for V for which (beta)[sup:frx0y6b8]*[/sup:frx0y6b8] is the dual basis.

i'm really not sure where to start here... i would really appreciate any help.
thank you all.

 

[pka]

Re: linear algebra

There no such a thing as standard notation in mathematics; this particularly true in the area of algebra. So if you post questions in linear algebra, then you must supply all definitions having to do with the problem. Otherwise, it is highly doubtful that anyone can help you.

 

[x3non25]

okay sorry about that. V is a finite-dimensional vector space. P[sub:28tuhfkv]1[/sub:28tuhfkv](R) polynomials of degree 1. f[sub:28tuhfkv]1[/sub:28tuhfkv] and f[sub:28tuhfkv]2[/sub:28tuhfkv] are functions belonging to the dual of V (V[sup:28tuhfkv]*[/sup:28tuhfkv]). beta is the standard ordered base for P[sub:28tuhfkv]1[/sub:28tuhfkv](R) and finally (beta)[sup:28tuhfkv]*[/sup:28tuhfkv] is the dual basis.
I hope this helps thank you