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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 / g by (/@g)() = (0) +g(0). If fis in V. define e Of by e f)(t) = ef(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 / g by (/@g)() = (0) +g(0). If fis in V. define e Of by e f)(t) = ef(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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Solve the following problems and show your complete solutions. Write it on a paper and do not type your answer.
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 / g by (/ @g)(n) = /(n) +g(1). If fis in V, define e of by e f)(t) = ef (1). 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 / g by (/ @g)(n) = /(n) +g(1). If fis in V, define e of by e f)(t) = ef (1). Prove that V is a vector space. (This is the vector space defined in Example 7.)
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