A population with three age classes has a Leslie matrix L =compute x₁, x₂, and x3.X1 =x3 =60090801010H54072183890957.610.90140 00.8 0If the initial population vector is xo =100100100

Answered: A population with three age classes has…

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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Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1.1 1.7 0.8 0 0 1.3] 0 L= 0 0.6 0 0 0 0 0.2 0 and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. λ1 = What is the long-term growth rate of this population of elk as a percent? growth rate = over/under 100%.) Are the elk thriving, static, or going extinct? ? (The growth rate is the percentage of growth
1. Let A be a 3x4 matrix. If nullity(A) = 3, rank(A) = 4. %3D 2. Let A be an n x n matrix. If the columns of A are linearly independent, then det(A) = 1. 3. If V is a 7-dimensional vector space and S is a set of 10 vectors, then the elements of S must be linearly dependent.
We want to train a mouse to follow a particular path in the maze (see image 1). To measure the effectiveness of the training, we want to compare the behaviour of the trained mouse to that of a mouse that runs through the maze at random.(a) Construct the matrix T describing the behaviour of the untrained mouse, where tij gives the probability of going to room i when the mouse is in room j. (Note that since the mouse moves randomly if it is in front of two doors, it has a 1/2 probability of going through each of these doors.) (b) Suppose the mouse begins its journey through the maze with a vector of probabilities P(0) = (see image 3) where pi(0) represents the probability of being in room i at the start; so of course we have p1(0)+p2(0)+p3(0)= 1). Show that the probabilities of being in room i after a change of room P(1) are given by P(1)=TP(0). Indications: proceed with a proof on the one hand and on the other hand: start by calculating the probabilities of being in parts 1,2 or 3 after…
Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1.1 1.7 1.3 0.8 0 0 0 L = 0 0.6 0 0 0 0 0.2 0 and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is xo = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = over/under 100%.) Are the elk thriving, static, or going extinct? ? (The growth rate is the percentage of growth
Given the matrix A = ag if A" A= a, I then -1 -1 2 O a. a = 9 O b. a4 = -2 And the values for a1, a2, a3 O c. a4 = -1 O d. a4 = 1 O O
How many determined (basic) variables does each augmented matrix have? [1 0 0 10] 8 a. Choose b. Choose C. Choose d. Choose 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 5 06 -10 0 00 1 0 1 001 0 0 3 10 0 0 -4 0 -6 4 0
A Leslie matrix is given below with the usual age groups, 0 year old (0-1), 1 year olds (1-2), etc. 0 2.5 07 0.6 0 Lo 0.4% Compute the population in years 1 and year 2 when the initial population has 100 newborns, 60 one-year- olds and 40 two-year-olds. X₁ =
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Given the Leslie matrix below, what is the population size after 2 timesteps given the starting population size of J= 10, T=10, A=100? Round to nearest whole number. J T A J 0.5 0.5 3.0 T 0.2 0 A O 0.2 0 O a. J=162; T=62; A=1 O b. J=10; T=10; A=100 O c. J=200; T=25; A=5 O d. J=310; T=2; A=3
6. For the given matrix M, shown below, find M. Please show your work and do not use the graphing calculator. M%3= 1 ftiokot prices 55
Find an LU factorization of the given matrix
A6

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A population with three age classes has a Leslie matrix L = compute x₁, x₂, and x3. X1 = x3 = 600 90 80 1010 H 540 72 1838 909 57.6 1 0.9 0 14 0 0 0.8 0 If the initial population vector is xo = 100 100 100