Step by Step solution about How to resolve the algorithm Cramer's rule step by step in the Python programming language

The provided code in Python implements a function det to calculate the determinant of a matrix and uses it to solve a system of linear equations. A step-by-step explanation of the code:

1. det(m, n) function:

   • This function calculates the determinant of a square matrix m of size n x n.
   • If n is 1 (a 1x1 matrix), it simply returns the single element in the matrix.
   • Otherwise, it uses the Laplace expansion method to calculate the determinant recursively.
   • It does this by removing each row from the matrix, multiplying the first element of each row by (-1)^r, and then recursively finding the determinant of the remaining matrix.
   • The final result is the sum of these products.

2. w is assigned to the length of the given list t.

3. d is assigned to the determinant of the matrix h using the det function.

4. The code checks if d is equal to 0. If it is, it means the system of linear equations has no unique solution, so it sets r to an empty list and exits.

5. If d is not 0, it calculates the solution to the system of linear equations.

   • It does this by creating a new matrix for each variable in t by replacing the first column of h with the corresponding column from t.
   • It then calculates the determinant of each of these new matrices and divides it by the original determinant d.
   • The result is a list r containing the solutions to the system of linear equations.

6. Finally, the code prints the list r.

def det(m,n):
 if n==1: return m[0][0]
 z=0
 for r in range(n):
  k=m[:]
  del k[r]
  z+=m[r][0]*(-1)**r*det([p[1:]for p in k],n-1)
 return z
w=len(t)
d=det(h,w)
if d==0:r=[]
else:r=[det([r[0:i]+[s]+r[i+1:]for r,s in zip(h,t)],w)/d for i in range(w)]
print(r)