Question: (a) Prove that the polynomials form an orthogonal basis for P2 with respect to the weighted inner product (b) Find the corresponding orthonormal basis. (c)

(a) Prove that the polynomials
(a) Prove that the polynomials form an orthogonal basis for P2

form an orthogonal basis for P2 with respect to the weighted inner product

(a) Prove that the polynomials form an orthogonal basis for P2

(b) Find the corresponding orthonormal basis.
(c) Write t2 as a linear combination of P0, P1, P2 using the orthogonal basis formula (5.7).

Po(t) = 1, P1(t) = t- 2 ,

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