Datasets:
| from fractions import Fraction as F | |
| A = [[1, 1, 1], [2, -1, 1], [1, 2, -1]] | |
| b = [6, 3, 2] | |
| m = [[F(value) for value in row] + [F(rhs)] for row, rhs in zip(A, b)] | |
| for col in range(3): | |
| pivot = next(r for r in range(col, 3) if m[r][col] != 0) | |
| m[col], m[pivot] = m[pivot], m[col] | |
| scale = m[col][col] | |
| m[col] = [value / scale for value in m[col]] | |
| for r in range(3): | |
| if r != col: | |
| factor = m[r][col] | |
| m[r] = [v - factor * p for v, p in zip(m[r], m[col])] | |
| solution = [m[i][-1] for i in range(3)] | |
| assert all(sum(F(a) * x for a, x in zip(row, solution)) == rhs for row, rhs in zip(A, b)) | |
| result = {"solution": [str(x) for x in solution]} | |
| import json | |
| print(json.dumps(result, ensure_ascii=False, sort_keys=True)) | |