To add gaussian elimination Implementation

[NithinU2802]

This PR is to add gaussian elimination implementation.

Steps Involved in the implementation:

• Construct the augmented matrix using the given inputs.
• Execute forward elimination to zero out elements below the pivot.
• Use back substitution to compute the variable values.
• Present the result as a solution vector x = [x, y, z] and Verification.

Closes #292 .

[Copilot]

Pull request overview

Adds a new Gaussian Elimination implementation in mathematics/ for solving linear systems Ax = b, and registers it in the repository directory listing (per issue #292).

Changes:

• Introduces gaussian_elimination(A, b) with forward elimination (partial pivoting) and back substitution.
• Adds an example + verification output for a 3×3 system.
• Updates DIRECTORY.md to include the new algorithm.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
mathematics/gaussian_elimination.r	New Gaussian elimination solver implementation + example usage/verification
DIRECTORY.md	Adds link entry for the new Gaussian Elimination script

[siriak]

Looks good, thanks!