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    Newton's Method Proof

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    Please show that when n=1, Newtons method given by:

    x^k=x^(k-1)-(J(x^(k-1))^-1)(F(x^(k-1)) for k>=1

    reduces to the familiar Newton's method given by:

    P_n=P_n-1 - f(p_n-1)/f'(P_n-1) for n>=1

    ^-1 is inverse
    J is the jacobian matrix
    The top equation is called newton's method for non linear systems. x is a vector. F(x_1,...,x_n)=(f_1(x_1,...,x_n),f_2(x_1,...,x_n),...,f_n(x_1,...,x_n)).

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    Solution Summary

    A Jacobian is employed in this Newton's Method proof. The solution is detailed and well presented.