Function solve_linear_system 

pub fn solve_linear_system(
    a: &Matrix<f64>,
    b: &Vec<f64>,
) -> Result<LinearSolution, String>

Solves a system of linear equations Ax = b.

This function constructs an augmented matrix [A | b], computes its Reduced Row Echelon Form (RREF), and then analyzes the RREF to determine the nature of the solution:

• Unique Solution: Returns a unique solution vector.
• Parametric Solution: Returns a particular solution and a basis for the null space.
• No Solution: Indicates an inconsistent system.

Arguments

• a - The coefficient matrix A.
• b - The constant vector b.

Returns

A Result containing a LinearSolution enum, or an error string.