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princess snowwhite

Member

Registered: 2012-11-06

Posts: 29

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

scientia

Member

Registered: 2009-11-13

Posts: 224

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 (2012-11-12 13:19:04)