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93237a0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | from itertools import permutations
from fractions import Fraction
A = [[1, 1, 1], [2, -1, 1], [1, 2, -1]]
b = [6, 3, 2]
def det(matrix):
total = 0
for p in permutations(range(3)):
inversions = sum(p[i] > p[j] for i in range(3) for j in range(i + 1, 3))
term = (-1) ** inversions
for i in range(3):
term *= matrix[i][p[i]]
total += term
return total
denominator = det(A)
assert denominator == 7
answer = []
for col in range(3):
replaced = [row[:] for row in A]
for r in range(3):
replaced[r][col] = b[r]
answer.append(str(Fraction(det(replaced), denominator)))
result = {"solution": answer}
import json
print(json.dumps(result, ensure_ascii=False, sort_keys=True))
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