need help plz

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- April 7th 2007, 10:59 AMharryLinear Dependence
need help plz

- April 7th 2007, 11:16 AMtopsquark
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