Let C[a, b] denotc the set of continuous functions f : [a, b] → R. Given any two functions S,9 € C[a, b], let (S, 9) = | S()g(t)dt. S(1)g(t)dt. Prove that the above bilincar form is bilincar, symmetric and positive (that is, (f, f) > 0 for all f € C[a, b]). You do not have to prove that this bilincar form is definite (that is, if (S, S) = 0, then f = 0).

Let C[a, b] denotc the set of continuous functions f : [a, b] → R. Given any two functions S,9 € C[a, b], let (S, 9) = | S()g(t)dt. S(1)g(t)dt. Prove that the above bilincar form is bilincar, symmetric and positive (that is, (f, f) > 0 for all f € C[a, b]). You do not have to prove that this bilincar form is definite (that is, if (S, S) = 0, then f = 0).

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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