Find the fundamental matrix F for the absorbing Markov chain, and find the product matrix FR.

**Solution**

To find F, begin by rewriting the transition matrix in the form P = by switching rows if necessary to get the absorbing state in the upper left corner and the non-absorbing states in the lower right corner.

P =

Thus ,Q = [0.8]and R = .

Next , F = . Since Q is a 1 x 1 matrix,=[1]and so F =

=

= 5

Finally, find FR.

FR = [5] .

.