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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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scientia
2012-11-13 12:14:15


Let
where
.


Then









.

This suggests that a basis for
is
.

All you have to do is to prove it. smile

NB: I've just shown that the set spans W; it remains for you to prove that it's linearly independent.

princess snowwhite
2012-11-13 06:36:32

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 roll

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