Numpy not solving matrix equation correctly

Question

In the code below, Is result not supposed to be the same as eqtn_ans[1] since numpy had no problem solving the simultaneous equation? Or I'm I missing something?

Since numpy was able to get the inverse of eqtn_coeffs doesn't that make the equation solvable?

import numpy as np

def solve_simultaneous_equation(eq_coef, ans):
        A = np.array(eq_coef)
        B = np.array(ans)
        E = np.linalg.solve(A,B)
        return E

eqtn_coeffs = [[0.13230431079864502, -0.4504314661026001, 0.6201357841491699], 
               [-0.04826474189758301, -0.4006437063217163, 1.5354962348937988], 
               [-0.22883379459381104, -0.3508559465408325, 2.4508566856384277]]

eqtn_ans = [0.0, 0.7853981852531433, 1.3258177042007446]

params = solve_simultaneous_equation(eqtn_coeffs, eqtn_ans)

result = np.dot(eqtn_coeffs[1],params)

print(result) # The result of this should be the same as eqtn_ans[1] 
              # but its not even though numpy was able to solve the equation.

result:

0.625

Answer 1

It is easy to see why you have a problem

np.linalg.det(eqtn_coeffs)

prints

3.3194268620340867e-17

If the determinant of a matrix is zero, then the linear system of equations it represents has no solution (to be mor precise, no desired unique solution). In other words, the system of equations contains at least two equations that are not linearly independent.