# | a11 a21 . . . an1 |    | x1 |    | b1 |
# |  .  .   . . .  .  |    |  . |    |  . |
# |  .  .   . . .  .  | \/ |  . | -- |  . |
# |  .  .   . . .  .  | /\ |  . | -- |  . |
# |  .  .   . . .  .  |    |  . |    |  . |
# | a1n a2n . . . ann |    | xn |    | bn |

# | a11 a21  . .    .     a'n1  |    | x1 |    | b1 |
# |  0  a'22 . .    .      .    |    |  . |    |  . |
# |  0   0   . .    .      .    | \/ |  . | -- |  . |
# |  0   0   . .    .      .    | /\ |  . | -- |  . |
# |  0   0   . . a'n-1n-1  .    |    |  . |    |  . |
# |  0   0   . .    0     a'nn  |    | xn |    | bn |


matrix = [[-1,  2,  1],
          [ 1, -3, -2],
          [ 3, -1, -1]]

bees = [-1, -1, 4]

n = len(matrix)
for row in range(1, n):
    fraction = matrix[row][0] / matrix[0][0]
    bees[row] -= fraction*bees[0]
    for col in range(n):
        matrix[row][col] -= fraction * matrix[0][col]

print(matrix)
print(bees)