Show that {1, cos t, cos 2 t,...,cos 6 t} is a linearly independent set of functions

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Show that {1, cos t, cos² t,...,cos⁶t} is a linearly independent set of functions defined on R. Use the method of Exercise 47.

Data from in Exercise 47

Show that {t, sin t, cos 2t, sin t cos t} is a linearly independent set of functions defined on R. Start by assuming that

Equation (5) must hold for all real t, so choose several specific values of t (say, t = 0, .1, .2) until you get a system of enough equations to determine that all the c_j must be zero.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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Question Posted: May 03, 2023 04:38 AM

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Show that {1, cos t, cos 2 t,...,cos 6 t} is a linearly independent set of functions

Question:

C₁t + C₂ sint + c3 cos 2t + c4 sint cost = 0 (5)

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For example writing c1 cost c3 costc4 costc5 costc costc7 cost0 with t 0 1 2 3 ...View the full answer

Linear Algebra And Its Applications

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