## Linear Combinations

{1, x, x(x-1), x(x-1)(x-2)} you want to find the linear combinations that will give you 1, x, x^2, x^3

a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = 1
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^2
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^3

I don't know what to do from there
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 Recognitions: Homework Help Science Advisor I think you might not want to call the constants all 'a'. 1=1 x=x as for the others trying writing out x(x-1) as something easier to work with
 If you set up an appropriate matrix and augmenting it with the answers you want, row reduction should give you your answers.

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