线性方程组直接解法——高斯消去法

#include<stdio.h>
#include<math.h>
#include<windows.h>
#define M 50
void input(double a[M][M + 1], int n);
void output(double x[M], int n);
void main(void)
{
    double a[M][M + 1], x[M], s;
    int i, j, k, n;
    printf("请输入原方程组的阶数：\n");
    scanf_s("%ld", &n);
    input(a, n);
    for (k = 0; k < n - 1; k++)
    {
        for (i = k + 1; i < n; i++)
        {
            a[i][k] /= -a[k][k];
            for (j = k + 1; j < n + 1; j++)
                a[i][j] += a[i][k] * a[k][j];
        }
    }
    for (k = n-1; k >= 0; k--)
    {
        s = 0;
        for (j = k + 1; j < n; j++)
            s += a[k][j] * x[j];
        x[k] = (a[k][n] - s) / a[k][k];
    }
    output(x, n);
    system("pause");
}
void input(double a[M][M+1],int n)
{
    int i, j;
    printf("请输入方程组的增广矩阵：\n");
    for (i = 0; i < n; i++)
    {
        for (j = 0; j < n+1; j++)
            scanf_s("%lf", &a[i][j]);
    }
}
void output(double x[M],int n)
{
    int k;
    printf("方程组的解为：\n");
    for (k = 0; k < n; k++)
        printf("%lf", x[k]);
}