SOLUTION: show that e^x and e^2x are independent.

Click here to see ALL problems on Linear Algebra

Question 608556: show that e^x and e^2x are independent.
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi, Note
A consistent system has at least one solution.
An inconsistent system has no solutions.
An independent system has exactly one solution.
A dependent system has infinitely many solutions.
show that e^x and e^2x are independent.(exactly one solution) (0,1)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Presuming you mean linearly independent, let be a vector space of all functions of a real variable .

Suppose and are two real numbers such that

If and are linearly independent then and

Divide by since is never zero

hence must be independent of which only occurs when . Therefore as well.

John

My calculator said it, I believe it, that settles it