Rewrite the given absorbing stochastic matrix so that the absorbing states appear first, and identify the submatrices R and S.

Question

Rewrite the given absorbing stochastic matrix so that the absorbing states appear first, and identify the submatrices R and S. ​  ​

Quizplus · Accepted Answer

The absorbing states are states 3 and 4. We can rewrite the matrix as:

$\begin{pmatrix}
1 & 0 & 0 & 0 & 0\ 
0 & 1 & 0 & 0 & 0\ 
0.5 & 0 & 0 & 0.5 & 0\ 
0 & 0 & 0 & 1 & 0\ 
0 & 0 & 0 & 0 & 1
\end{pmatrix}$

From this, we can see that the submatrix R is:

$\begin{pmatrix}
0.5 & 0\ 
0 & 0
\end{pmatrix}$

And the submatrix S is:

$\begin{pmatrix}
0 & 0.5 & 0\ 
0 & 1 & 0\ 
0 & 0 & 0
\end{pmatrix}$

Option C is the only one that matches this matrix.

Rewrite the Given Absorbing Stochastic Matrix So That the Absorbing