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  1. # Name : Ananda Das;
  2. # ID : 230241053;
  3. # Lab : 3 , Problem : 04;
  4.  
  5. def get_matrix_minor(matrix, i, j):
  6.     return [row[:j] + row[j+1:] for row in (matrix[:i] + matrix[i+1:])]
  7.  
  8. def determinant(matrix):
  9.     if len(matrix) == 1:
  10.         return matrix[0][0]
  11.     if len(matrix) == 2:
  12.         return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]
  13.     det = 0
  14.     for c in range(len(matrix)):
  15.         det += ((-1)**c) * matrix[0][c] * determinant(get_matrix_minor(matrix, 0, c))
  16.     return det
  17.  
  18. def replace_column(matrix, col_index, new_col):
  19.     return [
  20.         [new_col[row] if col == col_index else matrix[row][col] for col in range(len(matrix))]
  21.         for row in range(len(matrix))
  22.     ]
  23.  
  24. def transpose(matrix):
  25.     return [[matrix[j][i] for j in range(len(matrix))] for i in range(len(matrix))]
  26.  
  27. def cofactor_matrix(matrix):
  28.     cofactors = []
  29.     for i in range(len(matrix)):
  30.         row = []
  31.         for j in range(len(matrix)):
  32.             minor = get_matrix_minor(matrix, i, j)
  33.             row.append(((-1) ** (i + j)) * determinant(minor))
  34.         cofactors.append(row)
  35.     return cofactors
  36.  
  37. def inverse_matrix(matrix):
  38.     det = determinant(matrix)
  39.     if det == 0:
  40.         return None
  41.     cofactors = cofactor_matrix(matrix)
  42.     adjoint = transpose(cofactors)
  43.     return [[adjoint[i][j] / det for j in range(len(matrix))] for i in range(len(matrix))]
  44.  
  45. def cramer_solver(A, B):
  46.     n = len(A)
  47.     detA = determinant(A)
  48.     if detA == 0:
  49.         return None, 0
  50.     solution = []
  51.     for i in range(n):
  52.         Ai = replace_column(A, i, B)
  53.         xi = determinant(Ai) / detA
  54.         solution.append(xi)
  55.     return solution, detA
  56.  
  57. # ------------ MAIN ------------
  58. n = int(input("Enter the order of square matrix: "))
  59. print("Enter coefficients of matrix A:")
  60. A = [list(map(float, input().split())) for _ in range(n)]
  61.  
  62. print("Enter constants of vector B:")
  63. B = list(map(float, input().split()))
  64.  
  65. solution, detA = cramer_solver(A, B)
  66. print(f"\nDeterminant of A: {detA:.3f}")
  67.  
  68. if detA == 0:
  69.     print("Matrix is singular; the system is not uniquely solvable.")
  70.     exit()
  71.  
  72. print("\nThe solution using Cramer's Rule:")
  73. for i, val in enumerate(solution):
  74.     print(f"x{i+1} = {val:.6f}")
  75.  
  76. # Inverse
  77. invA = inverse_matrix(A)
  78. print("\nInverse of matrix A:")
  79. for row in invA:
  80.     print(" ".join(f"{val:.4f}" for val in row))
  81.  
Success #stdin #stdout 0.08s 14036KB
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2
2 5
-3 1
11 -4
stdout
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Enter the order of square matrix: Enter coefficients of matrix A:
Enter constants of vector B:

Determinant of A: 17.000

The solution using Cramer's Rule:
x1 = 1.823529
x2 = 1.470588

Inverse of matrix A:
0.0588 -0.2941
0.1765 0.1176
https://ideone.com/hhIJHY
language:
Python 3 (python  3.12)
created:
5 days ago
visibility:
public

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