Markov Chains: Steady-state Probabilities App

My research project for Operations Research is using Markov Chains so I decided to create a Maple App for their new Mobius Project (www.maplesoft.com).  Anyone can view this app all you need access to is one of the 3 (preferential order):

1. Maple program
2. Maple Player (free)
3. Web browser (http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=10491137)

Once you have the application running you have the ability to enter an initial state vector along with a probability matrix.  You can ask for specific states to be solved or a range of states (even with interval jumps).  Computation is extremely fast, using the power of Maple.  I've used it for small probability matrices such as 3x3's but would love to hear about anyone using it for larger data sets.

Symbolically you can enter both vectors and matrices in any form acceptable to Maple (it uses a type check).  I recommend using the following:

[a0,a1,...,aN] - for a vector
[ [x11,x12,...,x1N],[x21,x22,...,x2N],...,[xM1,xM2,...,xMN] ] - for a matrix

I plan on adding additional problems to the app as long as it keeps it functional and readable.  If not I will create them as separate apps.  Any feedback is appreciated!

Download Maple Worksheet: http://mobius.maplesoft.com/maplenet/mobius/download.jsp?appId=10491137

Download Maple Player: http://www.maplesoft.com/downloads/SelectPlatform.aspx?hash=16420394A38E21C9131460C345468589

View embedded Maple Worksheet: http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=10491137