For the following transition matrices, what is the absorbing state(s)? $$\left| \begin{array} { l l l l }
0 & 0 & 2 / 3 & 1 / 3 \
0 & 1 & 0 & 0 \
3 / 4 & 1 / 4 & 0 & 0 \
1 & 0 & 0 & 0
\end{array} \right|$$
A) state 1
B) state 2
C) state 3
D) state 4
E) state 2 and 4

Question

For the following transition matrices, what is the absorbing state(s)? $$\left| \begin{array} { l l l l } 
0 & 0 & 2 / 3 & 1 / 3 \
0 & 1 & 0 & 0 \
3 / 4 & 1 / 4 & 0 & 0 \
1 & 0 & 0 & 0
\end{array} \right|$$
A) state 1
B) state 2
C) state 3
D) state 4
E) state 2 and 4

Quizplus · Accepted Answer

An absorbing state is a state that, once entered, cannot be left. In the given matrix, state 2 is represented by the row [0 1 0 0], indicating that it has a 100% probability of staying in state 2 once it is reached, making it the absorbing state.

For the Following Transition Matrices, What Is the Absorbing State(s) ∣002/31/301003/41/4001000∣\left| \begin{array} { l l l l } 0 & 0 & 2 / 3 & 1 / 3 \\0 & 1 & 0 & 0 \\3 / 4 & 1 / 4 & 0 & 0 \\1 & 0 & 0 & 0\end{array} \right|​003/41​011/40​2/3000​1/3000​​

For the Following Transition Matrices, What Is the Absorbing State(s) $\left| \begin{array} { l l l l } 0 & 0 & 2 / 3 & 1 / 3 \\0 & 1 & 0 & 0 \\3 / 4 & 1 / 4 & 0 & 0 \\1 & 0 & 0 & 0\end{array} \right|$