Let P⁴ have the inner product as in Example 5, and let p₀. p₁, p₂ be the orthogonal polynomials from that example. Using your matrix program, apply the Gram-Schmidt process to the set {p₀. p₁. p₂, t³, t⁴) to create an orthogonal basis for P⁴.

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EXAMPLE 5 Let V be P4 with the inner product in Example 2, involving evaluation of polynomials at -2, -1, 0, 1, and 2, and view P2 as a subspace of V. Produce an orthogonal basis for P₂ by applying the Gram-Schmidt process to the polynomials 1, t, and 1².