# hw3.7.3 - L with ±x i = P±x i-1 so ±x i = P i ±x(or the...

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Math 43, Fall 2007 Week 12: Finish suggested homework 10, . . . Graded Homework 12: Section 3.7 - 2, 4; and 4.6 - 7, 1 1 pg. 356; due Wed. Dec. 5 From 4.6 we will ONLY cover pp. 322-326 (Markov chains) and pp. 327-329 (population growth).

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2 Finally, we’ve gone over the text’s Example 3.46 from Section 3.7, pp. 228-231 and discussed Examples 3.65 and 3.66. In each case we have an initial state vector ±x 0 and then subsequent states ±x 1 , ±x 2 , . . . , ±x k , . . . The states are related by a transition probability matrix P (or by a Leslie matrix
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Unformatted text preview: L ) with ±x i = P±x i-1 , so ±x i = P i ±x (or the same equations with P replaced by L ). In each case we get a steady state given by an eigenvector of the matrix. For the cases that occur in the applications the matrix P can be diagonalized; resp. we only need the positive eigenvalue, and we determine the steady state (resp. rate). Finally, we observe that the material of 4.4 follows directly from our work on eigenvalues, eigenvectors and eigenspaces....
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hw3.7.3 - L with ±x i = P±x i-1 so ±x i = P i ±x(or the...

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