(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Test the set of {1, ln(2x), ln(x^2)} for linear independence in F, the set of all functions.

If it is linearly dependent, express one of the functions as a linear combination of the others.

2. Relevant equations

N/A

3. The attempt at a solution

I know if [ a(1) + b(ln(2x)) + c(ln(x^2)) = 0 ] implies [ a = b = c = 0 ], then the set is linearly independent. Otherwise, it is linearly dependent.

The book gives an example problem where you can plug in 0 for x and solve for the coefficients, which are then shown to be 0. But that doesn't really work here.

Plugged in x=1: a+b(ln2) + cln(1) =0 implies a + bln2 = 0.

It works neatly in the book example (sinx, cosx) but doesn't really in this case. I can't think of any way to go about doing this...

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# Homework Help: Test the set of functions for linear independence in F

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