Python Gaussian elimination with for loops

Gaussian Elimination is a method for solving systems of linear equations by transforming an augmented matrix into its row-echelon form or reduced row-echelon form. In this tutorial, we will walk through the process of implementing Gaussian Elimination using Python with for loops and provide a code example.
Before you start, you should have a basic understanding of linear algebra and Python programming.
Create an augmented matrix from the system of linear equations.
Use row operations to transform the matrix into its row-echelon form.
Continue these row operations for all rows and columns, moving from the top-left to the bottom-right of the matrix.
The matrix will be in row-echelon form when finished.
Back-substitute to find the solutions to the system of equations.
Let's implement Gaussian Elimination in Python with for loops. We will create a function that takes an augmented matrix as input and returns the solutions to the system of equations. Here's a step-by-step code example:
In this code, gaussian_elimination takes the augmented matrix as input, performs Gaussian Elimination, and returns the solutions to the system of equations.
Gaussian Elimination is a fundamental method for solving systems of linear equations. You can implement it in Python using for loops as demonstrated in this tutorial. This code can be extended to handle larger systems of equations or matrices of arbitrary size.
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