Chapter 6.3, Problem 13P

Using the rate equations (20) through (22), express, in matrix notation, the system of differential equations that describe diffusion on a one-dimensional lattice with reflecting boundaries consisting of $n=4$ lattice sites. Find the general solution of the resulting system and plot the components of each of the eigenvectors of matrix $\text{A}$ on the same set of co-ordinate axes. Which eigenvalue controls the long-term rate of decay toward equilibrium?