My Math Forum Linear independence of functions

 Linear Algebra Linear Algebra Math Forum

 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
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,305
Thanks: 962

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top