hw4.4.22

# hw4.4.22 - P (or by a Leslie matrix L ) with ±x i = P±x...

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Math 43, Fall 2007 Week 11: Finish suggested homework 10, . . . Graded Homework 11: Section 4.4 - #12, 16, pg. 307, due Wed. Nov. 28 (NOTE change of date.) Suggested Homework 11: start material for Hw 12, including 4.4 - 6, 8, 10; 4.6 - 3,7. From 4.6 we will ONLY cover pp. 322-326 (Markov chains) and pp. 327-329 (population growth).

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2 On Friday we went over the text’s Example 3.46 from Section 3.7, pp. 228-231. Today (Monday) we’re discussing 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
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Unformatted text preview: P (or by a Leslie matrix 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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## This note was uploaded on 02/29/2008 for the course MATH 43 taught by Professor Dodson during the Spring '08 term at Lehigh University .

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hw4.4.22 - P (or by a Leslie matrix L ) with ±x i = P±x...

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