Chapter 7 - Section 7.7 - Markov Systems - Exercises - Page 531: 8

$P=\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ \end{bmatrix}$

Write the $ij$th entry of $P$ as the probability of transition from the state $i$ to $j$: $1→1$: $0$ $1→2$: $1$ $1→3$: $0$ $2→1$: $0$ $2→2$: $0$ $2→3$: $1$ $3→1$: $1$ $3→2$: $0$ $3→3$: $0$ So: $P=\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ \end{bmatrix}$