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Math Help - Proof of linear independence

  1. #1
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    Smile Proof of linear independence

    I have a matrix A consisting of equations

    1 X1 X1^2 X1^3 ...... X1^m
    1 X2 X2^2 X2^3 ...... X2^m
    1 ...
    1 ...
    1 Xn Xn^2 Xn^3 ...... Xn^m

    I must show that the collumns of A are linearly independant if n > m and at least m + 1 of the numbers X1, X2, X3 ... Xn are distinct.

    I am having trouble creating an algebraic proof for this, can anyone offer any insight?

    thanks very much
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  2. #2
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    Quote Originally Posted by Algebah View Post
    I have a matrix A consisting of equations

    1 X1 X1^2 X1^3 ...... X1^m
    1 X2 X2^2 X2^3 ...... X2^m
    1 ...
    1 ...
    1 Xn Xn^2 Xn^3 ...... Xn^m

    I must show that the collumns of A are linearly independant if n > m and at least m + 1 of the numbers X1, X2, X3 ... Xn are distinct.

    I am having trouble creating an algebraic proof for this, can anyone offer any insight?

    thanks very much
    Use the Fundamental Theorem of Algebra which gives the number of roots of a polynomial.
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