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# Following along the line of Exercise 11 in Section 6.3 and Exercise 15 in Section 7.2

ISBN: 9780534392000 331

## Solution for problem 9.2.19 Chapter 9-2

Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Problem 9.2.19

Following along the line of Exercise 11 in Section 6.3 and Exercise 15 in Section 7.2, suppose that a species of beetle has a life span of 4 years, and that a female in the first year has a survival rate of 1 2 , in the second year a survival rate of 1 4 , and in the third year a survival rate of 1 8 . Suppose additionally that a female gives birth, on the average, to two new females in the third year and to four new females in the fourth year. The matrix describing a single females contribution in one year to the female population in the succeeding year is A = 0024 1 2 000 0 1 4 0 0 0 0 1 8 0 , where again the entry in the ith row and jth column denotes the probabilistic contribution that a female of age j makes on the next years female population of age i. a. Use the Gersgorin Circle Theorem to determine a region in the complex plane containing all the eigenvalues of A. b. Use the Power method to determine the dominant eigenvalue of the matrix and its associated eigenvector. c. Use Algorithm 9.4 to determine any remaining eigenvalues and eigenvectors of A. d. Find the eigenvalues of A by using the characteristic polynomial of A and Newtons method. e. What is your long-range prediction for the population of these beetles?

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##### ISBN: 9780534392000

Numerical Analysis (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780534392000. This textbook survival guide was created for the textbook: Numerical Analysis (Available Titles CengageNOW) , edition: 8. The answer to “Following along the line of Exercise 11 in Section 6.3 and Exercise 15 in Section 7.2, suppose that a species of beetle has a life span of 4 years, and that a female in the first year has a survival rate of 1 2 , in the second year a survival rate of 1 4 , and in the third year a survival rate of 1 8 . Suppose additionally that a female gives birth, on the average, to two new females in the third year and to four new females in the fourth year. The matrix describing a single females contribution in one year to the female population in the succeeding year is A = 0024 1 2 000 0 1 4 0 0 0 0 1 8 0 , where again the entry in the ith row and jth column denotes the probabilistic contribution that a female of age j makes on the next years female population of age i. a. Use the Gersgorin Circle Theorem to determine a region in the complex plane containing all the eigenvalues of A. b. Use the Power method to determine the dominant eigenvalue of the matrix and its associated eigenvector. c. Use Algorithm 9.4 to determine any remaining eigenvalues and eigenvectors of A. d. Find the eigenvalues of A by using the characteristic polynomial of A and Newtons method. e. What is your long-range prediction for the population of these beetles?” is broken down into a number of easy to follow steps, and 240 words. Since the solution to 9.2.19 from 9-2 chapter was answered, more than 209 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 69 chapters, and 1072 solutions. The full step-by-step solution to problem: 9.2.19 from chapter: 9-2 was answered by , our top Calculus solution expert on 03/05/18, 08:28PM.

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