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Math Help - Population model

  1. #1
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    Population model

    The question is stated exactly as follows:

    "Suppose A has a strictly dominant eigenvalue \lambda_1. Age class evolution is given by: x^{(k)} = Ax^{(k-1)}. Initial Population is x^{(0)}.

    Initially, let x^{(0)} be the linear combination a_1x_1 + a_2x_2 + ... + a_nx_n, of A's linearly independent eigenvectors, with each constant a_i \neq 0. Find two expressions for the population distribution x^{(1)} after one generation; one using products involving matrix A, the other in terms of A's eigenvalues."

    Now, the question is a little blurry, and so I've come to an answer of which i'm not sure if is correct...

    My Answer:

    Expression #1 => x^{(1)} = Ax^{(0)}
    Expression #2 => x^{(1)} = \lambda x^{(0)}

    Please indicate for me if I'm wrong...and if so could you please direct me on how i should go about this question.

    Many thanks
    Last edited by tsal15; February 3rd 2009 at 02:36 AM.
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  2. #2
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    Melbourne
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    Quote Originally Posted by tsal15 View Post
    The question is stated exactly as follows:

    "Suppose A has a strictly dominant eigenvalue \lambda_1. Age class evolution is given by: x^{(k)} = Ax^{(k-1)}. Initial Population is x^{(0)}.

    Initially, let x^{(0)} be the linear combination a_1x_1 + a_2x_2 + ... + a_nx_n, of A's linearly independent eigenvectors, with each constant a_i \neq 0. Find two expressions for the population distribution x^{(1)} after one generation; one using products involving matrix A, the other in terms of A's eigenvalues."

    Now, the question is a little blurry, and so I've come to an answer of which i'm not sure if is correct...

    My Answer:

    Expression #1 => x^{(1)} = Ax^{(0)}
    Expression #2 => x^{(1)} = \lambda x^{(0)}

    Please indicate for me if I'm wrong...and if so could you please direct me on how i should go about this question.

    Many thanks
    Or should I expand the multiplication of the above?
    Last edited by tsal15; February 3rd 2009 at 02:36 AM.
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