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Proved that the set V of all real valued functions is a vector space under the operations defined in Exercise 13. Exercise 13: Let V be the set of all real-valued continuous functions. If f and g are in V, define f g by (f@g)() = f()+g(0). If f is in V. define c Of by (c Of)(t) = cf (1). Prove that V is a vector space. (This is the vector space defined in Example 7.)

Proved that the set V of all real valued functions is a vector space under the operations defined in Exercise 13. Exercise 13: Let V be the set of all real-valued continuous functions. If f and g are in V, define f g by (f@g)() = f()+g(0). If f is in V. define c Of by (c Of)(t) = cf (1). Prove that V is a vector space. (This is the vector space defined in Example 7.)

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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Exercise 2.2 Proved that the set V of all real valued functions is a vector space under the operations defined in Exercise 13. Exercise 13: Let V be the set of all real-valued continuous functions. If f and g are in V, define f g by ( @g) () = f()+g(0). If f is in V. define c Of by (c Of)(t) = cf(t). Prove that V is a vector space. (This is the vector space defined in Example 7.)
Transcribed Image Text:Exercise 2.2 Proved that the set V of all real valued functions is a vector space under the operations defined in Exercise 13. Exercise 13: Let V be the set of all real-valued continuous functions. If f and g are in V, define f g by ( @g) () = f()+g(0). If f is in V. define c Of by (c Of)(t) = cf(t). Prove that V is a vector space. (This is the vector space defined in Example 7.)
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