Question

Consider the stochastic matrix [0.1 0.2 0.3] A=[0.2 0.3 0.4] [0.7 0.5 0.3] Find the steady-state vector w for A. Write each entry of w as a fraction

Answer 1

To find the steady-state vector w for the given stochastic matrix A, we need to solve the equation Aw = w. The resulting steady-state vector w will be the null space solution or the solution obtained after row reduction.

Step-by-step explanation:

To find the steady-state vector w for the given stochastic matrix A, we need to solve the equation Aw = w. In this case, the equation becomes:

[0.1 0.2 0.3]w = w
[0.2 0.3 0.4]w = w
[0.7 0.5 0.3]w = w

Since w is a steady-state vector, it satisfies the equation Aw = w. This equation can be rewritten as (A - I)w = 0, where I is the identity matrix. We can solve this equation by finding the null space of (A - I) or by performing row reduction on (A - I). The resulting steady-state vector w will be the null space solution or the solution obtained after row reduction.