申論題

4.Eigen value and matrix diagonization
Afinite state machine (FSM) has two states: state S1 and state S2. Let Prob(S₁ →S₂) denote the
probability that the machine moves from state S1 to state S2 in a cycle. Assume that the state
transition probabilities are fixed in every cycle: Prob(S₁→S₁)=0.3, Prob(S₁→＞S₂)-0.7,
Prob(S₂→S₁)=0.6, Prob(S₂→S₂)=0.4. Initially, the FSM is in state S1 at cycle 0.

(a) Give a matrix A representing the state transition probabilities.