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Exercise 2.A.11 Proof. - Stanford University

Proof. We will show that p 0 = 1 p 1 = x p 2 = x3 + x2 p 3 = x3 is a basis for P 3(F). Note that none of these polynomials has degree 2. Proposition 2.42 in the book states that if V is a nite dimensional vector space, and we have a spanning list of vectors of length dimV, then that list is a basis. It is shown in the book that P 3(F) has ...

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