Science:Math Exam Resources/Courses/MATH307/December 2006/Question 03 (a)/Statement

Consider the discrete dynamical system

${\begin{bmatrix}a_{n+1}\\b_{n+1}\\c_{n+1}\end{bmatrix}}={\frac {1}{6}}{\begin{bmatrix}1&3&2\\2&1&1\\3&2&3\end{bmatrix}}{\begin{bmatrix}a_{n}\\b_{n}\\c_{n}\end{bmatrix}}$

which describes the evolution of the vector ${\begin{bmatrix}a&b&c\end{bmatrix}}^{T}$

Explain what a Markov matrix (stochastic matrix) is and why the coefficient matrix of this discrete dynamical system is a Markov matrix.