function x=nagauss(a,b,flag)

In this article, we will explore in detail methods for solving linear equation systems, including the Sequential Gaussian Elimination method. The Sequential Gaussian Elimination method is a popular numerical algorithm that can efficiently solve large-scale linear equation systems. The fundamental concept of this approach involves transforming the linear equation system into an upper triangular matrix, followed by back substitution to determine the values of unknown variables. Although this method may be slower compared to alternative approaches, its advantage lies in solving large linear equation systems through straightforward matrix operations, thereby conserving computational time and resources. From an implementation perspective, this algorithm typically involves three main phases: forward elimination to create zeros below the pivot elements, pivoting (when enabled by the flag parameter) to improve numerical stability, and back substitution to compute the solution vector. The function parameters 'a' represents the coefficient matrix, 'b' is the constant vector, while the 'flag' parameter controls optional partial pivoting functionality to handle potential numerical instability issues.