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ote the set of all real-valued continuous func g = f(t) +g(t) and c©f = c f(t) for all sc C[a,b] is a real vector space. %3D the set of all functions in C[a,b] such that f(a n of Cla bl?

ote the set of all real-valued continuous func g = f(t) +g(t) and c©f = c f(t) for all sc C[a,b] is a real vector space. %3D the set of all functions in C[a,b] such that f(a n of Cla bl?

Advanced Engineering Mathematics
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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1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b], we define fOg = f(t) +g(t) and cOf = c f (t) for all scalars c. Show that C[a,b] is a real vector space. b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be I| а. %3D a subspace of C[a,b]?
Transcribed Image Text:1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b], we define fOg = f(t) +g(t) and cOf = c f (t) for all scalars c. Show that C[a,b] is a real vector space. b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be I| а. %3D a subspace of C[a,b]?
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