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# Why does numpy calculate matrix determinant incorrectly

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I think this way. The determinant must be zero, I checked it on a piece of paper and in online calculators. But this code gives a response like this `5.329070518200744e-15 `.
What am I doing wrong? Maybe somewhere I was inattentive, and if not, what is the best way to calculate?

I guess it might depend on Python versions and especially Numpy versions.
In Google Colaboratory exactly 0.0 comes out, even if you print 64 decimal places.
I tried to put a different data type (by default, this matrix turns out to be `numpy.int64 `), for example `numpy.int16 `or `numpy.float32 `– no difference , it still comes out 0.0 .
But `numpy.float16 `cannot be set, `linalg `swears at it that it does not work with it.
But check for fun what kind of data you get in the matrix:

``````print (type (A [0,0]))
``````

In Google Colaboratory such versions are:

``````Python 3.6.9
Numpy 1.18.5
``````

The code with which I checked everything:

``````import numpy as np
A = np.array ([[1, 1, 2, -1],
[2, -1, 0, -5],
[-1, -1, 0, -2],
[6, 3, 4, -3]] #, dtype = np.float32)
)
print (np .__ version__)
print (type (A [0,0]))
print (np.linalg.det (A))
print (f "{np.linalg.det (A) :. 64f}")
``````

Result:

``````1.18.5
& lt; class 'numpy.int64' & gt;
0.0
0.000000000000000000000000000000000000000000000000000000000000
``````

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