Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state.
Empirical data show that if the particle is in State 1, then it is 2 times more likely to go to State 2 at the next step than to State 3. If it is in State 2, then it is 9 times more likely to go to State 3 at the next step than to State 1. If it is in State 3 then it is equally likely to go to State 1 or State 2 at the next step.
Let A be transition matrix for this markov chain. Find a₃₁, a₃₂, and a₃₃ (i.e., find the last row in the transition matrix)