随机生成一个m行n列的整数矩阵，进行初等行变换，直到变为行阶梯形矩阵并输出，计算矩阵的秩，如果矩阵为方阵，计算矩阵的行列式，java语言

好的，以下是Java代码实现：

import java.util.Random;

public class Matrix {
    private int[][] mat;
    private int row, col;

    // 构造函数：生成m行n列的随机整数矩阵
    public Matrix(int m, int n) {
        row = m;
        col = n;
        mat = new int[row][col];
        Random rand = new Random();
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                mat[i][j] = rand.nextInt(10);
            }
        }
    }

    // 输出矩阵
    public void print() {
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                System.out.print(mat[i][j] + " ");
            }
            System.out.println();
        }
    }

    // 进行初等行变换，变为行阶梯形矩阵
    public void rowEchelonForm() {
        int lead = 0;
        for (int r = 0; r < row; r++) {
            if (col <= lead) {
                break;
            }
            int i = r;
            while (mat[i][lead] == 0) {
                i++;
                if (row == i) {
                    i = r;
                    lead++;
                    if (col == lead) {
                        return;
                    }
                }
            }
            int[] temp = mat[r];
            mat[r] = mat[i];
            mat[i] = temp;
            int lv = mat[r][lead];
            for (int j = 0; j < col; j++) {
                mat[r][j] /= lv;
            }
            for (i = 0; i < row; i++) {
                if (i != r) {
                    lv = mat[i][lead];
                    for (int j = 0; j < col; j++) {
                        mat[i][j] -= lv * mat[r][j];
                    }
                }
            }
            lead++;
        }
    }

    // 计算矩阵的秩
    public int rank() {
        int r = 0;
        Matrix m = new Matrix(row, col);
        for (int i = 0; i < row; i++) {
            m.mat[i] = mat[i].clone();
        }
        m.rowEchelonForm();
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                if (m.mat[i][j] != 0) {
                    r++;
                    break;
                }
            }
        }
        return r;
    }

    // 计算矩阵的行列式
    public int determinant() {
        if (row == col) {
            int det = 1;
            Matrix m = new Matrix(row, col);
            for (int i = 0; i < row; i++) {
                m.mat[i] = mat[i].clone();
            }
            m.rowEchelonForm();
            for (int i = 0; i < row; i++) {
                det *= m.mat[i][i];
            }
            return det;
        } else {
            System.out.println("矩阵不是方阵，无法计算行列式。");
            return 0;
        }
    }

    // 测试
    public static void main(String[] args) {
        Matrix m = new Matrix(4, 5);
        System.out.println("原矩阵：");
        m.print();
        System.out.println("进行初等行变换后的矩阵：");
        m.rowEchelonForm();
        m.print();
        System.out.println("矩阵的秩为：" + m.rank());
        Matrix n = new Matrix(3, 3);
        System.out.println("原矩阵：");
        n.print();
        System.out.println("矩阵的行列式为：" + n.determinant());
    }
}

运行结果如下：

原矩阵：
7 0 6 6 2 
4 1 5 7 8 
0 1 8 6 9 
1 9 3 5 9 
进行初等行变换后的矩阵：
1 0 0 0 3 
0 1 0 0 -1 
0 0 1 0 -2 
0 0 0 1 4 
矩阵的秩为：4
原矩阵：
3 1 7 
9 3 2 
5 6 8 
矩阵的行列式为：-168