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Math Help - linear dependence/independence

  1. #1
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    linear dependence/independence

    a)V is the vector space of all real valued functions defined on R. A = {2,sin^2(x), cos^2(x)}
    Is A linearly independent?

    b) V=C([-PI, PI]).
    A={sin x , sin 2x, .... sin nx}, where n is some natural number. Is A linealy independent?

    I am not sure how to work them out.
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  2. #2
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    If the Wronskian is non-zero at some point in an interval, then the associated functions are linearly independent on the interval.

    For (a) though, is one element a linear combination of the others? If so, then they are dependent.
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