Let p(x), q(x) E P2(R). Determine (with proof) if the function (p(x), q(r)) = p(–1)q(-1) + p(1)q(1) satisfies the properties of positivity, definiteness, and additivity of an inner product on P2(R).
Let p(x), q(x) E P2(R). Determine (with proof) if the function (p(x), q(r)) = p(–1)q(-1) + p(1)q(1) satisfies the properties of positivity, definiteness, and additivity of an inner product on P2(R).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. Let p(x), q(x) E P2(R). Determine (with proof) if the function
(p(x), q(x)) = p(-1)q(-1)+p(1)q(1)
satisfies the properties of positivity, definiteness, and additivity of an inner
product on P2(R).
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