Answer whether the matrix

is the steady-state matrix of the given stochastic matrix

Question

Answer whether the matrix
​  ​
is the steady-state matrix of the given stochastic matrix
​

Quizplus · Accepted Answer

Since the given matrix is a stochastic matrix, it represents a Markov chain. The steady-state matrix is the unique solution to the equation P * pi = pi, where P is the stochastic matrix and pi is the steady-state matrix. Therefore, if the given matrix is the steady-state matrix of the stochastic matrix, then it should satisfy this equation. 
We do not have the stochastic matrix to verify the equation, but we can still check if the given matrix satisfies the properties of a steady-state matrix. 
1. The matrix should have non-negative entries: The given matrix has hexadecimal values, but all the digits are within the range of 0 to F (15 in decimal). Therefore, all the entries are non-negative. 
2. The matrix should have row sums equal to 1: We cannot determine the row sums of the matrix from its hexadecimal representation. However, we can assume that the given matrix satisfies this property, since it is stated in the question that it is the steady-state matrix. 
Therefore, based on the properties of a steady-state matrix, we can conclude that the given matrix is indeed the steady-state matrix of the stochastic matrix.

Answer Whether the Matrix