# Help with figuring out Linear Dependency

## Homework Statement

Hello, I have been given a list of functions and I need to figure out if they are linearly dependent or not. I've been trying to solve the problems for a while but I cannot figure out which ones are wrong. The list of functions are on my webpage at: http://vantraveller.blogspot.ca/2013/09/linear-dependency-question.html [Broken]

## Homework Equations

http://vantraveller.blogspot.ca/2013/09/linear-dependency-question.html [Broken]

## The Attempt at a Solution

For sure, I know cos^2(x) and sin^2(x), x and x^2, 1+ln(x) and 1-ln(x) is linearly independent because they are not multiples of each other, but with regards to the others, I am not to sure.

## The Attempt at a Solution

Last edited by a moderator:

Related Calculus and Beyond Homework Help News on Phys.org
arildno
Homework Helper
Gold Member
Dearly Missed
Set up the equation that must govern linear (in)dependency.
Prove that the equation only holds when the coefficients for each function is set equal to zero.

Mark44
Mentor
For sure, I know cos^2(x) and sin^2(x), x and x^2, 1+ln(x) and 1-ln(x) is linearly independent because they are not multiples of each other, but with regards to the others, I am not to sure.
That's not a good reason. If you have two functions, it's easy to tell whether each is a multiple of the other, but with three or more functions, that thinking doesn't work any more. For example, {sin2(x), cos2(x), 1} is a linearly dependent set. No function is a multiple of any other in the set, but the equation c1 * sin2(x) + c2 * cos2(x) + c3 * 1 = 0 has a solution in which not all of the constants are zero.