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**princess snowwhite****Member**- Registered: 2012-11-06
- Posts: 29

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

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

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)*

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