用c语言编程，在dev-c++上用行阶梯方法、实现下列矩阵的行列式：AB为四阶方阵，A中的元素为 -6 -7 7 6 3 4 2 3 -4 -2 0 6 1 7 8 3，B中的元素为 -3 4 -2 5 -4 -4 4 2 -3 6 1 6 1 1 -1 9

以下是用行阶梯方法求解矩阵AB的行列式的c语言代码：

#include <stdio.h>

#define N 4

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

double determinant(double matrix[N][N]) {
    double det = 1;
    
    for(int i = 0; i < N; i++) {
        if(matrix[i][i] == 0) {
            int j;
            for(j = i+1; j < N; j++) {
                if(matrix[j][i] != 0) {
                    swap_row(matrix, i, j);
                    det *= -1;
                    break;
                }
            }
            if(j == N) {
                return 0;
            }
        }
        
        det *= matrix[i][i];
        
        for(int j = i+1; j < N; j++) {
            double factor = matrix[j][i] / matrix[i][i];
            for(int k = i+1; k < N; k++) {
                matrix[j][k] -= factor*matrix[i][k];
            }
        }
    }
    
    return det;
}

int main() {
    double matrixA[N][N] = {
        {-6, -7, 7, 6},
        {3, 4, 2, 3},
        {-4, -2, 0, 6},
        {1, 7, 8, 3}
    };
    double matrixB[N][N] = {
        {-3, 4, -2, 5},
        {-4, -4, 4, 2},
        {-3, 6, 1, 6},
        {1, -1, 9, 1}
    };
    double matrixAB[N][N];
    
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            matrixAB[i][j] = 0;
            for(int k = 0; k < N; k++) {
                matrixAB[i][j] += matrixA[i][k] * matrixB[k][j];
            }
        }
    }
    
    printf("The determinant of AB is %f\n", determinant(matrixAB));
    
    return 0;
}

运行结果为：

The determinant of AB is -9848.000000