Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
#1 2012-11-13 06:36:32
- princess snowwhite
- Member
Offline
dimension of a subspace
let V be a vector space of all polynomials with real coefficients with degree at most n where n>=2, consider the elements of V as a function from R to R. define W={p belongs to V∫egration 0 to 1 p(x) dx=0} , show thar W is a subspace of V and dim W= n.
I have proved that W is a subspace but couldnot prove that din W= n 
#2 2012-11-13 12:14:15
- scientia
- Full Member
Offline
Re: dimension of a subspace
Let where .
Then
.
This suggests that a basis for is .
All you have to do is to prove it.
NB: I've just shown that the set spans W; it remains for you to prove that it's linearly independent.
Last edited by scientia (2012-11-13 12:19:04)