Answered: Let B = {(1, 1, 1), (1, –1, 1), (0, 0,… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 34E

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Let B = {(1,1, 1), (1, – 1, 1), (0,0, 1)}, B' = {(2,2, 0), (0, 1, 1), (1,0, 1)}, and [x]p
[2 3 1]".
(a) Find the transition matrix from B to B'
(b) Find the transition matrix from B' to B
(c) Verify that the two transition matrices from (a) and (b) are inverses of each other.
(d) Find the coordinate matrix [xR

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For the transition matrix P, solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observation, then it is 3 times as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Researchers estimate that the particle is currently 4 times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on the estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in state 1 three weeks from now?
(a) find the transition matrix from B to B′, (b) find the transition matrix from B′ to B, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix [x]B, given the coordinate matrix [x]B′.
(a) Find the transition matrix from B, to B2 (b) Find the transition matrix from B, to B.
Let A be an n × n positive stochastic matrix withdominant eigenvalue λ1 = 1 and linearly independenteigenvectors x1, x2, . . . , xn, and let y0 be aninitial probability vector for a Markov chainy0, y1= Ay0, y2= Ay1, . . . Show that if y0 = c1x1 + c2x2 +· · ·+cnxn then the component c1 in the direction of the positive eigenvector x1 must be nonzero.
For the Leslie matrix a. Find the dominant eigenvector b.normalized eigenvector c. Growth/decay rate of the population and the long term percentages that result in the two classes
Find the transition matrix from B to B′.B = {(1, 1), (1, 0)}, B′ = {(1, 0), (0, 1)}
Given the bases B = { f1= sin x, f2= cos x } and B' = { g1= 2sinx+cosx, g2 = 3 cos x } for a continuous function space in R. a. Determine the transition matrix from B' = {g1, g2} to B= {f1,f2} b. Calculate the coordinate matrix [h]B' where h=2 sin x-5 cos x
In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e)
In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e) what restrictions on the initial population sizes ensures the long time survival of both species in the forest
For a 4×4 matrix whose top three rows are arbitrary and whose bottom row is (0, 0, 0, 1), show that the points (x, y, z, 1) and (hx, hy, hz, h) transform to the same point after homogenization.
Find the steady-state vector for the transition matrix in the attached picture. Thanks.

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