Using a transition matrix as input to a cummulative matrix

Hi,

I have a cummulative matrix (based on the help from a previous thread) which I use for deciding the probability of a program switching between values, but I'd like to use a simpler transition matrix as input (as people understand that a bit better).

Currently I have a matrix that looks like:

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Which I use to determine the probability of switching between r1, r2 and r3.

I'd like a user to be able to input three values

Probability when in Regime 1 of staying in Regime 1
Probability when in Regime 2 of staying in Regime 2
Probability when in Regime 3 of staying in Regime 3

And to calculate the corresponding probabilities as input to my cumulative matrix. Trouble is, I'm stuck on the math of how to do this.

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