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The question amount to determining whether the obtained solution is composed of integers. There are multiple ways to do so. Perhaps, the simplest perhaps one to check whether denominators of all elements of a solution equal to 1 - like this:

from itertools import permutations

P1 = matrix([[33,79,29,41,47],[79,27,39,79,44],[90,83,58,1,90],[38,32,13,15,96],[72,82,88,83,23]])

numbers = [73300,167887,243754,254984,458756]
combinations = permutations(numbers, len(numbers)) 

for i, combo in enumerate(combinations, 1):
    P2 = Matrix([[combo[0]], [combo[1]], [combo[2]], [combo[3]], [combo[4]]])
    solution = P1.solve_right(P2) 
    if all(t.denominator()==1 for t in solution):
        print(solution)

The question amount amounts to determining whether the obtained solution is composed of integers. There are multiple ways to do so. Perhaps, the simplest perhaps one to check whether denominators of all elements of a solution equal to 1 - like this:

from itertools import permutations

P1 = matrix([[33,79,29,41,47],[79,27,39,79,44],[90,83,58,1,90],[38,32,13,15,96],[72,82,88,83,23]])

numbers = [73300,167887,243754,254984,458756]
combinations = permutations(numbers, len(numbers)) 

for i, combo in enumerate(combinations, 1):
    P2 = Matrix([[combo[0]], [combo[1]], [combo[2]], [combo[3]], [combo[4]]])
    solution = P1.solve_right(P2) 
    if all(t.denominator()==1 for t in solution):
        print(solution)

The question amounts to determining whether the obtained solution is composed of integers. There are multiple ways to do so. Perhaps, the simplest perhaps one is to check whether denominators of all elements of a solution equal to 1 - like this:

from itertools import permutations

P1 = matrix([[33,79,29,41,47],[79,27,39,79,44],[90,83,58,1,90],[38,32,13,15,96],[72,82,88,83,23]])

numbers = [73300,167887,243754,254984,458756]
combinations = permutations(numbers, len(numbers)) 

for i, combo in enumerate(combinations, 1):
    P2 = Matrix([[combo[0]], [combo[1]], [combo[2]], [combo[3]], [combo[4]]])
    solution = P1.solve_right(P2) 
    if all(t.denominator()==1 for t in solution):
        print(solution)

The question amounts to determining whether the obtained solution is composed of integers. There are multiple ways to do so. Perhaps, the simplest perhaps one is to check whether denominators of all elements of a solution equal to 1 - like this:

from itertools import permutations

P1 = matrix([[33,79,29,41,47],[79,27,39,79,44],[90,83,58,1,90],[38,32,13,15,96],[72,82,88,83,23]])

numbers = [73300,167887,243754,254984,458756]
combinations = permutations(numbers, len(numbers)) 

for i, combo in enumerate(combinations, 1):
    P2 = Matrix([[combo[0]], [combo[1]], [combo[2]], [combo[3]], [combo[4]]])
    solution = P1.solve_right(P2) 
    if all(t.denominator()==1 for t in solution):
        print(solution)