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

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 Question 608556: show that e^x and e^2x are independent.Found 2 solutions by ewatrrr, solver91311:Answer by ewatrrr(10682)   (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(16897)   (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