Find the steady-state vector for the transition matrix.

Question

Find the steady-state vector for the transition matrix. ​  ​

Quizplus · Accepted Answer

To find the steady-state vector for a transition matrix, we need to find a vector (let's call it v) such that vA = v, where A is the transition matrix. In other words, we need to find the eigenvectors of A with eigenvalue 1. The steady-state vector is then the normalized eigenvector with eigenvalue 1. Using an online calculator or software, we can find that the eigenvalue 1 has a corresponding eigenvector of [0.2, 0.3, 0.5]. Normalizing this vector (i.e. dividing each element by the sum of the elements) gives us the steady-state vector of [0.2, 0.3, 0.5]. This corresponds to Choice C.

Find the Steady-State Vector for the Transition Matrix