/// Represents a solver for systems of linear equations using the Gaussian Elimination method.
/// This class applies Gaussian Elimination to transform the matrix into row echelon form and then performs back substitution to find the solution vector.
/// This implementation is based on: https://www.algorithm-archive.org/contents/gaussian_elimination/gaussian_elimination.html
/// This implementation is based on: <see href="https://www.algorithm-archive.org/contents/gaussian_elimination/gaussian_elimination.html"/>