Solution
= Solution
On the closed class, the transition <matrix> is
$$
\begin{pmatrix}1/3&2/3\\1/4&3/4\end{pmatrix}.
$$
Its <stationary distribution> is $(3/11,8/11)$. The class is irreducible and aperiodic because of its self-loops, while the other class is transient and enters it almost surely. Hence
$$
\lim_{n\to\infty}P^n=
\begin{pmatrix}
0&3/11&0&8/11\\0&3/11&0&8/11\\0&3/11&0&8/11\\0&3/11&0&8/11
\end{pmatrix}.
$$