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Math Help - Using the Wronskian to prove linear (in)dependence

  1. #1
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    Using the Wronskian to prove linear (in)dependence

    Hi,

    Please could someone confirm if I've does this question correctly or not?

    Thanks

    Find out whether or not the functions x, e^x and xe^x are linearly dependent.

    So, the Wronskian of those functions works out to be:
    (x-2)e^{2x}
    which is equal to zero when x=2, so the functions are linearly dependent then?
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  2. #2
    Super Member girdav's Avatar
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    Re: Using the Wronskian to prove linear (in)dependence

    Yes, it's correct.
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Re: Using the Wronskian to prove linear (in)dependence

    Quote Originally Posted by girdav View Post
    Yes, it's correct.
    But W=(x-2)e^{2x} \neq 0 for all x.
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  4. #4
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    Re: Using the Wronskian to prove linear (in)dependence

    No. If the functions were dependent, the Wronskian would be identically 0, not just 0 at a single point.
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