# NumPy linalg.det – Compute the determinant of the given array

Hello and welcome to this tutorial on Numpy linalg.det. In this tutorial, we will be learning about the NumPy linalg.det() method and also seeing a lot of examples regarding the same. So let us begin!

Also check: Numpy linalg.eig – Compute the eigenvalues and right eigenvectors of a square array

## What is numpy.linalg.det?

The `numpy.linalg.det()` method in NumPy is used to compute the determinant of a given square matrix.

If we have a 2×2 matrix of the form:

Its determinant is calculated as:

For a 3×3 matrix like

The determinant is computed as:

Similarly, we can calculate the determinant of higher-order arrays.

## Syntax of NumPy linalg.det

```numpy.linalg.det(a)
```
• Parameter: a, an MxM array. Input array to compute the determinant of.
• Returns: Determinant of a.

## Examples of NumPy linalg.det

Let’s look at some examples of the NumPy linalg.det function to learn how it works.

### 1. Using NumPy linalg.det on a 2×2 array

```import numpy as np

arr = [[2, 1], [3, 5]]
# using np.linalg.det() method to compute the determinant
print("array = ", arr)
print("Determinant of array = ", np.linalg.det(arr))
det = 5*2 - 3*1
print("Determinant of array using manual calculation = ", det)
```

Output:

```array =  [[2, 1], [3, 5]]
Determinant of array =  6.999999999999999
Determinant of array using manual calculation =  7
```

### Using NumPy linalg.det on a 2×2 array with negative numbers

```import numpy as np

arr = [[-5, 2], [-4, 8]]
# using np.linalg.det() method to compute the determinant
print("array = ", arr)
print("Determinant of array = ", np.linalg.det(arr))
det = (-5*8) - (-4*2)
print("Determinant of array using manual calculation = ", det)
```

Output:

```array =  [[-5, 2], [-4, 8]]
Determinant of array =  -32.0
Determinant of array using manual calculation =  -32
```

### NumPy linalg.det calculation for a 3×3 array

```import numpy as np

arr = [[2, 1, 3], [5, 3, 4], [1, 0, 1]]
# using np.linalg.det() method to compute the determinant
print("array = ", arr)
print("Determinant of array = ", np.linalg.det(arr))
det = 2*(3*1 -0*4) -1*(5*1 - 1*4) + 3*(5*0 - 3*1)
print("Determinant of array using manual calculation = ", det)
```

Output:

```array =  [[2, 1, 3], [5, 3, 4], [1, 0, 1]]
Determinant of array =  -4.0
Determinant of array using manual calculation =  -4
```

In all the above examples, we have used the `numpy.linalg.det` method to compute the determinant as well as calculated the determinant using the manual method i.e. through the formulas discussed above. Through this, we can conclude that both methods return the same answer.

## Conclusion

That’s all! In this tutorial, we learned about the Numpy linalg.det method and practiced different types of examples using the same.