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I have five sets of three functions that I need to test for linear independence. I know that I could write them as a linear combination of scalar multiples of the functions, set it equal to 0 and see if I can solve for the scalar multiples. To clarify I mean:

Functions:

[tex]cos(x),cos(2x),cos(3x)[/tex]

[tex]a_{1}cos(x)+a_{2}cos(2x)+a_{3}cos(3x)=0[/tex]

Since the only solutions to that equation are a_1=a_2=a_3=0, the functions are linearly independent.

I also know that I could use the Wronskian of the functions, but this is time consuming and can lead to meaningless information.

Does anyone know of a more efficient method to determine if 3 functions are linearly independent or dependent?

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# Homework Help: Linear Independence

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