Matrix Determinant

The determinant of a matrix is a scalar value computed from a square matrix that gives us some very useful information. For example, it can tell us whether an inverse of a matrix exists. If the determinant of a matrix is zero, there is no inverse for a matrix. This also tells us useful information about solving linear equations.

Given matrix $A$ such that:

$$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$

then

$$det(A) = det(\begin{bmatrix} a & b \\ c & d \end{bmatrix}) = ad - bc$$

Implementation in Numpy

The numpy.linalg.det method returns the determinant of a matrix

import numpy as np

A = np.array([3, 5, 1, 2, 5, 3, 3, 2, 1]).reshape(3,3)
A

array([[3, 5, 1], [2, 5, 3], [3, 2, 1]])

np.linalg.det(A)

21.00000000000001