Transition Matricies

A transition matricies question has the info moving around(students changing their minds over what restaruaunt they prefer). There is a chart showing what people stay at which restaraunt, and what ones they switch to.
The first step is to create a nXn matrix using decimal equivalents to show the switches and input them in the calculator. Headers for the rows and columns are very important to keep track of.
The second step is to create a row matrix with either A)Real # values or B) the % of some distribution, which is also put in the calculator.
The third and final step is to multiply the row matrix by the nXn matrix which gives you the answer of the next transition. This can be continued until stability is reached. To prove stability you can do the transition to the power of 50, then 51 to see if any digits change.