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Linear Combinations

  1. Dec 1, 2004 #1
    {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
  2. jcsd
  3. Dec 1, 2004 #2

    matt grime

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    I think you might not want to call the constants all 'a'.

    as for the others trying writing out x(x-1) as something easier to work with
  4. Dec 5, 2004 #3
    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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