Problem 11. Let F(R, R) be the vector space over R of all functions f: R → R. Provethat if a, b e R are distinct, then the functions f(x) eax and g(x)ebx are linearlyindependent.==1

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Answered: Problem 11. Let F(R, R) be the vector…

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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Problem 11. Let F(R, R) be the vector space over R of all functions f: RR. Prove that if a, b e R are distinct, then the functions f(x) = eax and g(x) ebx are linearly = independent.