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



 

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