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May 15th, 2019, 09:52 AM  #1 
Member Joined: Apr 2017 From: India Posts: 73 Thanks: 0  Linear independence of functions
Whether Cos 3x and Cos (3x + Pi/2)are linearly independent or not in the interval (infinity, infinity)? My attempt: I calculated the Wronskian that comes out to be 3 (independent of x) that signifies that this function is linearly independent because the sufficient condition for the set of functions to be linearly independent is the nonvanishing of Wronskian for atleast one point in the interval. Am I correct? 
May 15th, 2019, 10:45 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
May 15th, 2019, 01:32 PM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 600 Thanks: 88 
Since the cos and sin are two different trigonometric functions then it proves it but the general method requires Wronskian calculation .


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functions, independence, linear 
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