Question

An nn matrix is called a positive markov matrix if each element is positive and the sum of the elements in each column is 1. write the following function to check whether a matrix is a markov matrix: def ismarkovmatrix (m): write a main function that prompts the user to enter a matrix of numbers and tests whether it is a markov matrix. here are some sample runs : enter a 3 by 3 matrix row by row : 0.15 0.875 0.375 0.55 0.005 0.225 0.30 0.12 0.4 it is a markov matrix enter a 3 by 3 matrix row by row: 0.95 -0.875 0.375 0.65 0.005 0.225 0.30 0.22 -0.4 it is not a markov matrix

A) def ismarkovmatrix(matrix):
B) def checkmarkov(matrix):
C) def is_markov(matrix):
D) def verify_markov(matrix):

Answer 1

Option C: To check whether a matrix is a positive Markov matrix, you can use the provided Python function which verifies if each element is positive and if the sum of elements in each column is 1.

Step-by-step explanation:

To check whether a matrix is a positive Markov matrix, you can use the following Python function:

def is_markov_matrix(matrix):
# Check if each element is positive
for row in matrix:
for element in row:
if element <= 0:
return False

# Check if the sum of elements in each column is 1
column_sums = [sum(column) for column in zip(*matrix)]
for sum in column_sums:
if sum != 1:
return False

return True

In the provided code, the function is_markov_matrix takes a matrix as input and checks if each element is positive and if the sum of elements in each column is 1. If any of these conditions are not met, the function returns False indicating that the matrix is not a positive Markov matrix. Otherwise, it returns True.