In Exercise 15 of Section 6.3, we assumed that the contribution a female beetle of a
Chapter 7, Problem 17(choose chapter or problem)
In Exercise 15 of Section 6.3, we assumed that the contribution a female beetle of a certain type made to the future years beetle population could be expressed in terms of the matrix A = 006 1 2 0 0 0 1 3 0 , where the entry in the ith row and jth column represents the probabilistic contribution of a beetle of age j onto the next years female population of age i. a. Does the matrix A have any real eigenvalues? If so, determine them and any associated eigenvectors. b. If a sample of this species was needed for laboratory test purposes that would have a constant proportion in each age group from year to year, what criteria could be imposed on the initial population to ensure that this requirement would be satisfied?
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