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 May 15th, 2019, 09:52 AM #1 Member   Joined: Apr 2017 From: India Posts: 74 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 non-vanishing of Wronskian for atleast one point in the interval. Am I correct? May 15th, 2019, 10:45 AM   #2
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 Originally Posted by shashank dwivedi 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 non-vanishing of Wronskian for atleast one point in the interval. Am I correct?
Yes. Also $\displaystyle cos \left ( 3x + \dfrac{\pi}{2} \right ) = sin(3x)$ which makes this a bit easier on the calculation. (At least in my own mind.)

-Dan May 15th, 2019, 01:32 PM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 742 Thanks: 98 Since the cos and sin are two different trigonometric functions then it proves it but the general method requires Wronskian calculation . Tags functions, independence, linear Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Luiz Linear Algebra 7 August 29th, 2015 12:54 PM Luiz Linear Algebra 1 August 26th, 2015 09:22 AM Luiz Linear Algebra 5 August 24th, 2015 02:10 PM Luiz Linear Algebra 1 August 24th, 2015 10:45 AM autumn94 Linear Algebra 1 March 29th, 2015 02:14 PM

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