Using MATLAB, complete the following question:

The dining hall at a student residence offers three options for breakfast: Option A, Option B and Option C. On each day each student chooses exactly one option. Din- ing hall management performed a study of how a choice of an option on any given day influences the choice of an option on the immediately following day, and it made the following observations: Among those students who choose Option A on a given day, 80% will choose Op- tion A on the following day, and the remaining students will split their choices equally between Option B and Option C. Among those students who choose Option B on a given day, 70% will choose Op- tion B on the following day, and the remaining students will split their choices equally between Option A and Option C. Among those students who choose Option C on a given day, 60% will choose Op- tion C on the following day, and all remaining students will choose Option B. Model this dynamical system as a Markov chain. Write down the transition matrix. The dining hall at a student residence offers three options for breakfast: Option A, Option B and Option C. On each day each student chooses exactly one option. Din- ing hall management performed a study of how a choice of an option on any given day influences the choice of an option on the immediately following day, and it made the following observations: Among those students who choose Option A on a given day, 80% will choose Op- tion A on the following day, and the remaining students will split their choices equally between Option B and Option C. Among those students who choose Option B on a given day, 70% will choose Op- tion B on the following day, and the remaining students will split their choices equally between Option A and Option C. Among those students who choose Option C on a given day, 60% will choose Op- tion C on the following day, and all remaining students will choose Option B. Model this dynamical system as a Markov chain. Write down the transition matrix