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# Solved: Let A be an n n positive stochastic matrix with dominant eigenvalue 1 = 1 and

ISBN: 9780321962218 437

## Solution for problem 13 Chapter 6.8

Linear Algebra with Applications | 9th Edition

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Linear Algebra with Applications | 9th Edition

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Problem 13

Let A be an n n positive stochastic matrix with dominant eigenvalue 1 = 1 and linearly independent eigenvectors x1, x2, ... , xn, and let y0 be an initial probability vector for a Markov chain y0, y1 = Ay0, y2 = Ay1, ... (a) Show that 1 = 1 has a positive eigenvector x1. (b) Show that yj1 = 1, j = 0, 1, .... (c) Show that if y0 = c1x1 + c2x2 ++ cnxn then the component c1 in the direction of the positive eigenvector x1 must be nonzero. (d) Show that the state vectors yj of the Markov chain converge to a steady-state vector. (e) Show that c1 = 1 x11 and hence the steady-state vector is independent of the initial probability vector y0.

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Elementary Statistics Math 124-08 Vera Klimkovsky 21 September 2016 Chapter 4 – Scatter plots and Correlation Chapter 4 – Scatter plots and Correlation Scatter plot ( XY plot)  3 ways to describe a scatter plot: o Form: Linear or Nonlinear o Direction: Positive or Negative ( could also be neither) o Strength: Strong, Moderate, Weak Ex: Two Quantitative...

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##### ISBN: 9780321962218

This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 9. Linear Algebra with Applications was written by and is associated to the ISBN: 9780321962218. This full solution covers the following key subjects: . This expansive textbook survival guide covers 47 chapters, and 935 solutions. The answer to “Let A be an n n positive stochastic matrix with dominant eigenvalue 1 = 1 and linearly independent eigenvectors x1, x2, ... , xn, and let y0 be an initial probability vector for a Markov chain y0, y1 = Ay0, y2 = Ay1, ... (a) Show that 1 = 1 has a positive eigenvector x1. (b) Show that yj1 = 1, j = 0, 1, .... (c) Show that if y0 = c1x1 + c2x2 ++ cnxn then the component c1 in the direction of the positive eigenvector x1 must be nonzero. (d) Show that the state vectors yj of the Markov chain converge to a steady-state vector. (e) Show that c1 = 1 x11 and hence the steady-state vector is independent of the initial probability vector y0.” is broken down into a number of easy to follow steps, and 128 words. The full step-by-step solution to problem: 13 from chapter: 6.8 was answered by , our top Math solution expert on 03/15/18, 05:26PM. Since the solution to 13 from 6.8 chapter was answered, more than 212 students have viewed the full step-by-step answer.

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