c) By solving a linear system of equations

In an ergodic Markov chain, the steady-state probabilities are found by solving a system of linear equations that arise from the condition that the probabilities of being in each state do not change over time (i.e., the steady-state distribution is unchanged by the transition matrix). This system typically involves setting up equations where the steady-state probabilities satisfy the condition πP=π\pi , where π\piπ is the steady-state vector and P is the transition matrix.