TEAM PROJECT. Linear Independence and Dependence. (a)
Chapter 3, Problem 3.1(choose chapter or problem)
TEAM PROJECT. Linear Independence and Dependence. (a) Investigate the given question about a set 5 of functions on an intervall. Give an example. Prove your answer. (I) If 5 contains the zero function, can 5 be linearly independent? (2) If 5 is linearly independent on a subinterval J of I. is it linearly independent on l? (3) If 5 is linearly dependent on a subinterval J of I. is it linearly dependent on n (4) If 5 is linearly independent on I, is it linearly independent on a subinterval J? (5) If 5 is linearly dependent on 1. is it linearly independent on a subinterval J? (6) If 5 is linearly dependent on I, and if T contains 5, is T linearly dependent on l? (b) In what cases can you use the Wronskian for testing linear independence? By what other means can you perform such a tcst'?
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