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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![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c86e56e-41ec-4f95-9739-742d2ba134eb%2Fb2acd4ac-6b97-49d7-b317-999e89da3e09%2Fhbe92p.png&w=3840&q=75)
Transcribed Image Text: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).
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