4. A Markov matrix M has each m, 20 and the sum of each column equal to 1. For a

given matrix M we can inspect its entries to determine if they are nonnegative and

MATLAB can be used to compute the sum of the columns. Type help sum for a

description of the command sum(M).

[134]

M1= 5 2 4

M3=

4 3 2

5 1 6 4

2 52.1

1 3 0 1

2 1 2 4

2 2 6]

M2 5 2 4

3.6.1

M4=

[3

21 46 4

2 59 24 1

3

2

2 19 1

1 11 4

a. Use MATLAB to determine which of M/ through M4 is a Markov matrix.

(indicate yes or no.)

MI

M2

M3

b. For those that are Markov matrices use eig to determine r = max

an eigenvalue. Record your results here.

M4

xwhere, & is

c. Complete the following using the terminology of the introduction to these

exercises.

Any process using a Markov matrix is

d. For each of the Markov matrices of Ml through M4 find the eigenvector

corresponding tor from part b. How are these eigenvectors related to your

conjecture in part e? Be specific.