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Math Help - Show that a set of functions is linearly independent

  1. #1
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    Show that a set of functions is linearly independent

    Hello everybody

    I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent.

    My attempt :

    f(x) = k1 * e-t + k2 * e-it + k3 * et + k4 * eit

    f '(x) = k1 * -e-t + k2 * -ie-it + k3 * et + k4 * ieit

    f ''(x) = k1 * e-t + k2 * -e-it + k3 * et + k4 * -eit

    f(0) = k1 * 1 + k2 * 1 + k3 * 1+ k4 * 1 = 0

    f '(0) = k1 * -1 + k2 * -i + k3 * 1+ k4 * i = 0

    f ''(0) = k1 * 1 + k2 * -1 + k3 * 1+ k4 * -1 = 0

    But when I plot this in maple and reduce it I get this :

    Show that a set of functions is linearly independent-billede-1.png

    They're linearly dependent but this can't be correct. So I guess I'm doing something wrong but what ?

    I would really appreciate it if someone could help me.
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  2. #2
    MHF Contributor

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    Re: Show that a set of functions is linearly independent

    You have four functions so you need to look at the third derivative also so that you will have four equations in four unknowns.
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  3. #3
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    Re: Show that a set of functions is linearly independent

    I have solved this but thank you
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  4. #4
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    Re: Show that a set of functions is linearly independent

    But I'm wondering if you could help me with something else la this ?
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