I don't understand why I don't get the right stationary distribution/vector when I use the methods I know for this problem.
$A=\begin{pmatrix} 3/4&0&1/4 \\ 1/3&1/2&1/6 \\ 1&0&0 \end{pmatrix}$
For example, if I try to solve $\pi A = \pi$ (system of linear equations), I get:
$\pi = (3/4, 0, 1/4)$
And if I try to solve it with $(\pi A)^T = \pi ^T$ (via eigenvalues and vectors) I get even weirder results.
But if I calculate something like $A*A*A*A$, I finally come to the solution $\pi = (4/5, 0, 1/5)$, which fits when I insert the values in $\pi A = \pi$
Am I missing something? Can the methods only be used if the matrix is irreducible?