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 c©f = c f(t) for all scalars c. Show that C[a,b] is a real vector space. а. 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 a subspace of C[a,b]?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 c©f = c f(t) for all scalars c.
a. 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
%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 c©f = c f(t) for all scalars c. a. 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 %3D a subspace of C[a,b]?
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