@@ -10,6 +10,8 @@ def add(matrix_a, matrix_b):
1010matrix_c .append (list_1 )
1111return matrix_c
1212
13+ def scalarMultiply (matrix ,n ):
14+ return [[x * n for x in row ]for row in matrix ]
1315
1416def multiply (matrix_a ,matrix_b ):
1517matrix_c = []
@@ -24,13 +26,50 @@ def multiply(matrix_a, matrix_b):
2426matrix_c .append (list_1 )
2527return matrix_c
2628
29+ def identity (n ):
30+ return [[int (row == column )for column in range (n )]for row in range (n )]
31+
32+ def transpose (matrix ):
33+ return map (list ,zip (* matrix ))
34+
35+ def minor (matrix ,row ,column ):
36+ minor = matrix [:row ]+ matrix [row + 1 :]
37+ minor = [row [:column ]+ row [column + 1 :]for row in minor ]
38+ return minor
39+
40+ def determinant (matrix ):
41+ if len (matrix )== 1 :return matrix [0 ][0 ]
42+
43+ res = 0
44+ for x in range (len (matrix )):
45+ res += matrix [0 ][x ]* determinant (minor (matrix ,0 ,x ))* (- 1 )** x
46+ return res
47+
48+ def inverse (matrix ):
49+ det = determinant (matrix )
50+ if det == 0 :return None
51+
52+ matrixMinor = [[]for _ in range (len (matrix ))]
53+ for i in range (len (matrix )):
54+ for j in range (len (matrix )):
55+ matrixMinor [i ].append (determinant (minor (matrix ,i ,j )))
56+
57+ cofactors = [[x * (- 1 )** (row + col )for col ,x in enumerate (matrixMinor [row ])]for row in range (len (matrix ))]
58+ adjugate = transpose (cofactors )
59+ return scalarMultiply (adjugate ,1 / det )
2760
2861def main ():
2962matrix_a = [[12 ,10 ], [3 ,9 ]]
3063matrix_b = [[3 ,4 ], [7 ,4 ]]
64+ matrix_c = [[11 ,12 ,13 ,14 ], [21 ,22 ,23 ,24 ], [31 ,32 ,33 ,34 ], [41 ,42 ,43 ,44 ]]
65+ matrix_d = [[3 ,0 ,2 ], [2 ,0 ,- 2 ], [0 ,1 ,1 ]]
66+
3167print (add (matrix_a ,matrix_b ))
3268print (multiply (matrix_a ,matrix_b ))
33-
69+ print (identity (5 ))
70+ print (minor (matrix_c ,1 ,2 ))
71+ print (determinant (matrix_b ))
72+ print (inverse (matrix_d ))
3473
3574if __name__ == '__main__' :
3675main ()