document.write( "Question 608556: show that e^x and e^2x are independent. \n" ); document.write( "

Algebra.Com's Answer #383298 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Presuming you mean linearly independent, let

be a vector space of all functions of a real variable

.\r
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\n" ); document.write( "\n" ); document.write( "Suppose

and

are two real numbers such that\r
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\r
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\n" ); document.write( "\n" ); document.write( "If

and

are linearly independent then

and

\r
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\n" ); document.write( "\n" ); document.write( "Divide by

since

is never zero\r
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\r
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\n" ); document.write( "\n" ); document.write( "hence

must be independent of

which only occurs when

. Therefore

as well.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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