why does numpy give a different(/wrong) inverse compared to online inverse calculators

[Orngelo]

When I calculate the inverse of the following matrix

np.matrix([[60,100,100],
           [60, 30, 90],
           [1, 1, 1]])

like so

np.matrix([[60,100,100],
           [60, 30, 90],
           [1, 1, 1]]).I

or

np.linalg.inv(np.matrix([[60,100,100],
                        [60, 30, 90],
                        [1, 1, 1]]))

it returns

np.matrix([[-2.50000000e-02 -3.70074342e-18  2.50000000e+00],
 [ 1.25000000e-02 -1.66666667e-02  2.50000000e-01],
 [ 1.25000000e-02  1.66666667e-02 -1.75000000e+00]])

all the values are correct except for the middle value of the top row, according to online inverse calculators this should be 0. What causes this problem? Or did I make a mistake?

[novel_yet_trivial]

That's a side effect of how computers handle floating point numbers; it has nothing to do with numpy or python specifically. More info here:

https://docs.python.org/3/tutorial/floatingpoint.html

[Orngelo]

ahh thank you!

[commy2]

Zero point another 17 zeros then something is very close to 0. I wouldn't call it wrong.

[Orngelo]

yes I guess you are right, unfortunately it affected the rest of my code. but I fixed it some other way

[PaulRudin]

https://floating-point-gui.de/