import numpy as np


if __name__ == '__main__':

    A = np.array([[1,0,2],
                  [0,1,0],
                  [1e-4,0,1e-4]])
    b_exact = np.array([[1],[1],[0]])
    b_approx = np.array([[1],[1],[1.67e-7]])
    print("Inverse von A:\n", np.linalg.inv(A))
    x_exact = np.linalg.solve(A,b_exact)
    print(x_exact)
    x_approx = np.linalg.solve(A,b_approx)
    print(x_approx)
    print(x_exact-x_approx)

    print("Task 1 d:")

    print(60003*(3e-7/3))
    print((60003/(1-0.0060003))*((3e-7/3)+(1.67e-7/1)))
    print(((0.01*(1-0.0060003))/60003)-(3e-7/3))