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Unformatted text preview: MATH129A, Linear Algebra I Project 2 Due in class on 4/5/2010 (M) Read the description of the spotted owl population at the beginning of Chapter 5 (page 301 302). To summarize, these owls have three distinct life stages: juvenile (first year), subadult (second year) and adult (third year and older). Let x k = j k s k a k and A = . 33 t 0 0 . 71 0 . 94 where j k , s k and a k denote the number of owls in each stage in year k , t is the survival rate of owls from juvenile to subadult, and x k +1 = A x k . In the text it is reported that the population will eventually die out if t = 0 . 18 but not if t = 0 . 30 . You will verify these facts in questions 1 and 2. We will use eigenvalues and eigenvectors to understand the dynamics of this population. 1. Let t = 0 . 18. Suppose there are 100 owls in each life stage in 2007, and so x = 100 100 100 . Input the matrix A with the given value of t and the vector x into the software MATLAB as follows, >> A=[0, 0, .33;.18, 0, 0;0, .71, .94] (then hit enter to see the matrix A) >> x0=[100, 100, 100] (then hit enter to see the vector x0)...
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