Let S be the subspace P3 consisting of all polynomials P(x) such that p(0) = 0, and let T be the subspace of all polynomials q(x) such that q(1) = 0. Find a basis for S, T and S[tex]\cap[/tex]T
The Attempt at a Solution
I know that a basis is formed by linearly independant vectors which also generate the space thay belong to. And is true for polynomials that L.I. can be drawn for the coeff matrix that results from the vector grouping the terms by the powers of X.
What I am not sure is what p(0) = 0 and q(1) = 0 means. Is it 0, 0X, 0X^2 = 0 and 1, x, x^2 = 0?
I know it is supposed to be a simple question or at least that's how I see it, but I took my last math course about 7 years ago, and I can't find a resource to clarify that for the moment.
Thanks for your help.