Given the following transition probability matrices for Markov chains:

Matrix $1$:

$([0\mathrm{.}7,0\mathrm{.}3],[0\mathrm{.}4,0\mathrm{.}6])$

Matrix $2$:

$([0\mathrm{.}5,0\mathrm{.}2,0\mathrm{.}3],[0\mathrm{.}1,0\mathrm{.}6,0\mathrm{.}3],[0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}5])$

Page $1$

Homework $5$

Operations Research II

IE $4390$

Matrix $3$:

$([0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}2,0\mathrm{.}1],[0\mathrm{.}2,0\mathrm{.}5,0\mathrm{.}2,0\mathrm{.}1],[0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}2],[0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4])$

For each matrix:

$($a$)$ Identify any absorbing states.

$($b$)$ Determine which states are transient.

$($c$)$ Classify the recurrent states.