5. In unit 2 assessment Problem 9, you investigated the populations of three age groups of an animal species that lived to a maximum of two years, using the transition matrix [0.559 0.6 0.1] A= 0.7 0 0 0 0.3 0 The problem of determining the stable distribution for each age group can best be solved using eigenvalues and eigenvectors. a. What are the eigenvalues of A? b. Determine an eigenvector u corresponding to eigenvalue = 1. c. Determine an eigenvector u corresponding to eigenvalue λ=1 that has positive entries. d. Determine an eigenvector и corresponding to eigenvalue 2 = 1 that has positive entries and the sum of the entries is equal to 1. e. Use the vector in part d) to determine the percentage of animal species that will eventually have current age zero. current age one. current age two.
5. In unit 2 assessment Problem 9, you investigated the populations of three age groups of an animal species that lived to a maximum of two years, using the transition matrix [0.559 0.6 0.1] A= 0.7 0 0 0 0.3 0 The problem of determining the stable distribution for each age group can best be solved using eigenvalues and eigenvectors. a. What are the eigenvalues of A? b. Determine an eigenvector u corresponding to eigenvalue = 1. c. Determine an eigenvector u corresponding to eigenvalue λ=1 that has positive entries. d. Determine an eigenvector и corresponding to eigenvalue 2 = 1 that has positive entries and the sum of the entries is equal to 1. e. Use the vector in part d) to determine the percentage of animal species that will eventually have current age zero. current age one. current age two.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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d, e
![5. In unit 2 assessment Problem 9, you investigated the populations of three age groups of
an animal species that lived to a maximum of two years, using the transition matrix
[0.559 0.6 0.1]
0 0
0.3 0
The problem of determining the stable distribution for each age group can best be solved
using eigenvalues and eigenvectors.
a. What are the eigenvalues of A?
b. Determine an eigenvector u
corresponding to eigenvalue = 1.
c. Determine an eigenvector u corresponding to eigenvalue λ=1 that has positive
entries.
A = 0.7
0
d. Determine an eigenvector и corresponding to eigenvalue 2 = 1 that has positive
entries and the sum of the entries is equal to 1.
e. Use the vector in part d) to determine the percentage of animal species that will
eventually have
current age zero.
current age one.
current age two.
f. Look at the plots you created for the population trends in U2 problem 9. Do the
trends match the eigen-analysis you just stepped through? How so?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cafdb60-7d1d-4699-94a3-8fee7de7f9f5%2F4182a878-06fb-4ddc-920a-7965d89a9275%2F8pb6u8b_processed.png&w=3840&q=75)
Transcribed Image Text:5. In unit 2 assessment Problem 9, you investigated the populations of three age groups of
an animal species that lived to a maximum of two years, using the transition matrix
[0.559 0.6 0.1]
0 0
0.3 0
The problem of determining the stable distribution for each age group can best be solved
using eigenvalues and eigenvectors.
a. What are the eigenvalues of A?
b. Determine an eigenvector u
corresponding to eigenvalue = 1.
c. Determine an eigenvector u corresponding to eigenvalue λ=1 that has positive
entries.
A = 0.7
0
d. Determine an eigenvector и corresponding to eigenvalue 2 = 1 that has positive
entries and the sum of the entries is equal to 1.
e. Use the vector in part d) to determine the percentage of animal species that will
eventually have
current age zero.
current age one.
current age two.
f. Look at the plots you created for the population trends in U2 problem 9. Do the
trends match the eigen-analysis you just stepped through? How so?
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