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Math Help - Linear Dependence

  1. #1
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    Linear Dependence

    need help plz
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  2. #2
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    Quote Originally Posted by harry View Post
    need help plz
    You need to show that it is possible to construct at least one of the elements from a linear combination of the other three.

    For example, let's try to construct
    -5 = a(5sin^2(x)) + b(cos^2(x)) + c(tan(x))
    where a, b, and c are constants.

    Note that sin^2(x) + cos^2(x) = 1 is a constant, so let c = 0 and a = -1 and b = -5:

    -1*(5sin^2(x)) + -5*(cos^2(x)) + 0*tan(x) = -5*(sin^2(x) + cos^2(x)) = -5*1 = -5

    So a linear combination of two elements of the set makes a third element of the set. Thus the set is linearly dependent.

    -Dan
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