用列主元高斯消去法、Jacobi 迭代法、Gauss-Seidel 迭代法解如下方程组输出方程组的解，及矩阵 L 和 U。

好的，这是一个更加复杂的问题，需要分步骤来实现。以下是代码实现：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define N 3
#define MAX_ITER 10000
#define TOLERANCE 1e-5

void printMatrix(double matrix[N][N+1]) {
    for(int i=0; i<N; i++) {
        for(int j=0; j<N+1; j++) {
            printf("%.2f ", matrix[i][j]);
        }
        printf("\n");
    }
}

void swapRow(double matrix[N][N+1], int i, int j) {
    for(int k=0; k<N+1; k++) {
        double temp = matrix[i][k];
        matrix[i][k] = matrix[j][k];
        matrix[j][k] = temp;
    }
}

void LUPDecomposition(double matrix[N][N+1], double L[N][N], double U[N][N]) {
    for(int i=0; i<N; i++) {
        for(int j=0; j<N; j++) {
            if(j<i) {
                L[j][i] = 0;
            } else {
                L[j][i] = matrix[j][i]/matrix[i][i];
                for(int k=0; k<i; k++) {
                    matrix[j][k] = matrix[j][k] - L[j][i]*matrix[i][k];
                }
            }
        }
        for(int j=i; j<N; j++) {
            U[i][j] = matrix[i][j];
        }
    }
}

int gaussianElimination(double matrix[N][N+1], double solution[N]) {
    double L[N][N], U[N][N];
    LUPDecomposition(matrix, L, U);
    printf("L:\n");
    printMatrix(L);
    printf("\nU:\n");
    printMatrix(U);
    printf("\n");

    for(int i=0; i<N; i++) {
        int maxRow = i;
        for(int j=i+1; j<N; j++) {
            if(abs(matrix[j][i]) > abs(matrix[maxRow][i])) {
                maxRow = j;
            }
        }
        if(i != maxRow) {
            swapRow(matrix, i, maxRow);
        }
        if(matrix[i][i] == 0) {
            return 0;
        }
        for(int j=i+1; j<N; j++) {
            double factor = matrix[j][i]/matrix[i][i];
            for(int k=i+1; k<N+1; k++) {
                matrix[j][k] = matrix[j][k] - factor*matrix[i][k];
            }
        }
    }

    for(int i=N-1; i>=0; i--) {
        solution[i] = matrix[i][N];
        for(int j=i+1; j<N; j++) {
            solution[i] = solution[i] - matrix[i][j]*solution[j];
        }
        solution[i] = solution[i]/matrix[i][i];
    }

    return 1;
}

int jacobi(double matrix[N][N+1], double solution[N]) {
    double x[N], x_new[N];
    for(int i=0; i<N; i++) {
        x[i] = 0;
    }

    int iter = 0;
    double error = TOLERANCE + 1;

    while(iter < MAX_ITER && error > TOLERANCE) {
        for(int i=0; i<N; i++) {
            double sum = 0;
            for(int j=0; j<N; j++) {
                if(j != i) {
                    sum = sum + matrix[i][j]*x[j];
                }
            }
            x_new[i] = (matrix[i][N] - sum)/matrix[i][i];
        }

        error = 0;
        for(int i=0; i<N; i++) {
            error = error + pow(x_new[i] - x[i], 2);
            x[i] = x_new[i];
        }
        error = sqrt(error);

        iter++;
    }

    if(iter == MAX_ITER) {
        return 0;
    } else {
        for(int i=0; i<N; i++) {
            solution[i] = x[i];
        }
        return 1;
    }
}

int gaussSeidel(double matrix[N][N+1], double solution[N]) {
    double x[N];
    for(int i=0; i<N; i++) {
        x[i] = 0;
    }

    int iter = 0;
    double error = TOLERANCE + 1;

    while(iter < MAX_ITER && error > TOLERANCE) {
        for(int i=0; i<N; i++) {
            double sum = 0;
            for(int j=0; j<N; j++) {
                if(j != i) {
                    sum = sum + matrix[i][j]*solution[j];
                }
            }
            solution[i] = (matrix[i][N] - sum)/matrix[i][i];
        }

        error = 0;
        for(int i=0; i<N; i++) {
            error = error + pow(solution[i] - x[i], 2);
            x[i] = solution[i];
        }
        error = sqrt(error);

        iter++;
    }

    if(iter == MAX_ITER) {
        return 0;
    } else {
        return 1;
    }
}

int main() {
    double matrix[N][N+1] = {{2, -1, 1, 8}, {-3, -1, 2, -11}, {-2, 1, 2, -3}};
    double solution[N];
    if(gaussianElimination(matrix, solution)) {
        printf("Gaussian elimination:\n");
        for(int i=0; i<N; i++) {
            printf("%.2f\n", solution[i]);
        }
        printf("\n");
    } else {
        printf("No unique solution.\n");
    }

    if(jacobi(matrix, solution)) {
        printf("Jacobi:\n");
        for(int i=0; i<N; i++) {
            printf("%.2f\n", solution[i]);
        }
        printf("\n");
    } else {
        printf("Jacobi method failed.\n");
    }

    if(gaussSeidel(matrix, solution)) {
        printf("Gauss-Seidel:\n");
        for(int i=0; i<N; i++) {
            printf("%.2f\n", solution[i]);
        }
        printf("\n");
    } else {
        printf("Gauss-Seidel method failed.\n");
    }

    return 0;
}

这个程序通过列主元高斯消去法、Jacobi迭代法和Gauss-Seidel迭代法求解一个3x3的线性方程组，并输出方程组的解和矩阵L和U。你可以将输入的系数矩阵和常数向量修改为你自己的数据。注意：如果矩阵不可逆，则会输出“No unique solution.”。如果Jacobi或Gauss-Seidel方法无法收敛，则会输出“Jacobi method failed.”或“Gauss-Seidel method failed.”。