please look at the attachments.

A small correction to Problem 2 in PS10:  the matrix P should have 3/8, not 3/9, as the value for the (5,6) entry.  This will make the row sum to one.    Thanks to the student who pointed that out!

Also, please make sure you are interpreting Problem 1 consistent with the graph figure.  For example, the probability p₁₄  (i=1, j=4) should be zero since there is no edge between 1 and 4.