Question

A 3x3 Markov matrix with more than one steady state.

a) A Markov matrix is always of size 3x3.
b) Steady states in a 3x3 Markov matrix are not possible.
c) There can be more than one steady state in a 3x3 Markov matrix.
d) Markov matrices are only applicable to 2x2 systems.

Answer 1

There can be more than one steady state in a 3x3 Markov matrix. The answer is option C.

Step-by-step explanation:

c) There can be more than one steady state in a 3x3 Markov matrix.

a) This statement is false. A Markov matrix can be of any size, not necessarily 3x3. The size of a Markov matrix depends on the number of states in the Markov chain.

b) This statement is false. Steady states are possible in a 3x3 Markov matrix. Steady states are solutions to the equation Px= x, where P is the Markov matrix and x is the steady state vector.

c) This statement is true. A 3x3 Markov matrix can have more than one steady state. Steady states are the eigenvectors associated with the eigenvalue 1. If there are multiple linearly independent eigenvectors associated with the eigenvalue 1, there can be more than one steady state.

d) This statement is false. Markov matrices can be applied to systems of any size, not limited to 2x2 systems. The size of the matrix depends on the number of states in the Markov chain.