[Feat] To add Gaussian Elimination Algorithm for Solving Linear Systems

[NithinU2802]

Gaussian Elimination Implementation

Hi Team,

I would like to add a Gaussian Elimination implementation to the repository. Gaussian Elimination is a fundamental and widely used algorithm for solving systems of linear equations. It works by transforming the coefficient matrix into an upper triangular form and then applying back substitution to compute the solution. This algorithm is essential in many areas such as scientific computing, data analysis, engineering, and numerical methods.

Steps Involved:

1. Create the augmented matrix
2. Perform forward elimination to make the lower triangular part zero
3. Apply the substitution method to find the values
4. Obtain the solution in the form of x = [x, y, z]

Example:

Consider the system of equations:

2x + 3y − z = 5
4x + 4y − 3z = 3
2x − 3y + z = −1

Using Gaussian Elimination, this system can be systematically reduced and solved to obtain the unique solution:

x = 1, y = 2, z = 3

I’m happy to get assigned and raise a PR for this🚀.