Which of the following is/are true for a Markov chain Xk+1 Axk, k = 0, 1,2, ..., where A is an n x n stochastic matrix? (Select all that apply) ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Ak p approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.

Which of the following is/are true for a Markov chain Xk+1 Axk, k = 0, 1,2, ..., where A is an n x n stochastic matrix? (Select all that apply) ✔The sum of each row of A is 1. If A is regular, then A has a unique probability vector that is an eigenvector corresponding to eigenvalue 1. If A is regular, then Ak p approaches the same probability vector for any probability vector p as k approaches infinity. If p is any probability vector, then Ap is a probability vector. If A is regular, then A has 1 as an eigenvalue.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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