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Construct any 3 by 3 Markov matrix M: positive entries down each column add to 1. If e =

Chapter 5, Problem 5.1.32

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QUESTION:

Construct any 3 by 3 Markov matrix M: positive entries down each column add to 1. If e = (1,1,1), verify that MT e = e. By 11, = 1 is also an eigenvalue of M. Challenge: A 3 by 3 singular Markov matrix with trace 1 2 has eigenvalues = .

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QUESTION:

Construct any 3 by 3 Markov matrix M: positive entries down each column add to 1. If e = (1,1,1), verify that MT e = e. By 11, = 1 is also an eigenvalue of M. Challenge: A 3 by 3 singular Markov matrix with trace 1 2 has eigenvalues = .

ANSWER:

Step 1 of 3

The objective is to construct a  Markov matrix M. Such that positive entries down each column add up to 1. The Markov matrix provides a complete way to understand the probabilities of each step in a Markov chain.

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