import numpy as np

for n in [3,5,10,100,1000]:
    A = np.zeros((n,n))
    x = np.zeros((n,1))
    y_c = np.zeros((n,1))

    for i in range(0,n):
        x[i] = i+1
        y_c[i] = (i+1) * n;

        for j in range(0,n):
            A[i,j] =(i+1) / (j+1)

    y = A@x
    
    if n == 3 or n == 5:
        print(x)
        print(A)
        print(y)

    print("Fuer n =",n,":",np.linalg.norm(y - y_c))