Question: (a) Prove that the polynomials form an orthogonal basis for the vector space P3 of cubic polynomials for the L2 inner product (b) Find an

(a) Prove that the polynomials
Po(1) = 1, P,() = 1, P2(1) = r? - . P3(1) = r³ – }

form an orthogonal basis for the vector space P3 of cubic polynomials for the L2 inner product

(a) Prove that the polynomials form an orthogonal basis for the

(b) Find an orthonormal basis of V3.
(c) Write t3 as a linear combination of P0, P1, P2, P3 using the orthogonal basis formula (5.7).

Po(1) = 1, P,() = 1, P2(1) = r? - . P3(1) = r }

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