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27-12-2023
Mathematics

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Define an inner product on P4 using the evaluation of polynomials at the points -2, -1, 0, 1, and 2. Find an orthonormal basis for P4. A) ⟨p,q⟩=p(−2)q(−2)+p(−1)q(−1)+p(0)q(0)+p(1)q(1)+p(2)q(2) B) ⟨p,q⟩=p(−2)q(−2)−p(−1)q(−1)+p(0)q(0)−p(1)q(1)+p(2)q(2) C) ⟨p,q⟩=∫−22p(x)q(x)dx D) ⟨p,q⟩=∑i=−22p(i)q(i)

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