**The determinant** is a mathematical property of a **square matrix** (matrix with equal number of columns and rows) that provides valuable information about the matrix.
The determinant is denoted as **det(A)** or **|A|**, where A represents the matrix. The determinant is a single value that can be positive, negative, or zero. 

The determinant carries several important properties and interpretations:

- **Invertibility**: A square matrix A is invertible (non-singular) if and only if its determinant is nonzero;
- **Area or Volume Scaling**: For 2x2 and 3x3 matrices, the determinant provides information about the scaling factor or the change in area/volume under a linear transformation represented by the matrix;
- **Linear Independence**: The determinant can determine whether a set of vectors is linearly independent. If the determinant of a matrix composed of vectors is nonzero, the vectors are linearly independent;
- **Solution Existence**: In systems of linear equations represented by matrices, the determinant can determine whether a unique solution exists. If the determinant is nonzero, a unique solution exists; otherwise, there may be no solution or an infinite number of solutions.

In Python, we can calculate determinant using `np.linalg.det()` method: 

import numpy as np

# Define a square matrix
A = np.array([[3, 1], [2, 4]])

# Calculate the determinant
det_A = np.linalg.det(A)

# Print the determinant
print(round(det_A, 2))

Can we calculate the determinant of the following matrix: `[[1, 2, -1], [2, 3, 9]]`?

To study many applied disciplines, it is necessary to have basic knowledge of higher mathematics and linear algebra. Mathematics is often used in data analysis, system modeling, building machine learning models, etc. Let's look at some of the most important topics and learn how to use the mathematical apparatus to solve real problems.

Let's start with some basic definitions and concepts we'll use later. Consider the idea of a function, a numerical sequence, and its sum, and also understand what a coordinate system's basis is.

The simplest and most commonly used type of relationship is the linear relationship. Linear algebra is a branch of higher mathematics entirely devoted to linear functions and linear spaces. Let's look at some of the most important topics in linear algebra: vectors, matrices, solving linear equations, and solving the spectral problem for matrices.

Mathematical analysis is a discipline that allows you to analyze functions according to various criteria. Consider how to check numerical sequences for convergence, find the maximum/minimum values of functions, solve nonlinear equations, and use integrals to solve applied problems.

Matrix Determinant