生成随机m行n列的随机整数矩阵，做初等行变换直至行阶梯形矩阵，java语言

以下是Java代码实现：

import java.util.Random;

public class RowReduction {
    public static void main(String[] args) {
        int m = 5; // 矩阵行数
        int n = 6; // 矩阵列数
        int[][] matrix = generateRandomMatrix(m, n); // 生成随机矩阵

        System.out.println("原始矩阵：");
        printMatrix(matrix);

        rowReduction(matrix); // 做初等行变换

        System.out.println("行阶梯形矩阵：");
        printMatrix(matrix);
    }

    // 生成随机矩阵
    public static int[][] generateRandomMatrix(int m, int n) {
        int[][] matrix = new int[m][n];
        Random rand = new Random();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                matrix[i][j] = rand.nextInt(10);
            }
        }
        return matrix;
    }

    // 打印矩阵
    public static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                System.out.print(matrix[i][j] + " ");
            }
            System.out.println();
        }
        System.out.println();
    }

    // 做初等行变换
    public static void rowReduction(int[][] matrix) {
        int lead = 0;
        int rowCount = matrix.length;
        int columnCount = matrix[0].length;
        for (int r = 0; r < rowCount; r++) {
            if (lead >= columnCount) {
                return;
            }
            int i = r;
            while (matrix[i][lead] == 0) {
                i++;
                if (i == rowCount) {
                    i = r;
                    lead++;
                    if (lead == columnCount) {
                        return;
                    }
                }
            }
            int[] temp = matrix[r];
            matrix[r] = matrix[i];
            matrix[i] = temp;

            int lv = matrix[r][lead];
            for (int j = 0; j < columnCount; j++) {
                matrix[r][j] /= lv;
            }

            for (int k = 0; k < rowCount; k++) {
                if (k != r) {
                    int lv2 = matrix[k][lead];
                    for (int j = 0; j < columnCount; j++) {
                        matrix[k][j] -= lv2 * matrix[r][j];
                    }
                }
            }
            lead++;
        }
    }
}

上述代码中，generateRandomMatrix() 方法用于生成随机矩阵，printMatrix() 方法用于打印矩阵，rowReduction() 方法用于做初等行变换。在 rowReduction() 方法中，我们采用高斯-约旦消元法，将矩阵转化为行阶梯形矩阵。最后，我们可以调用这些方法，生成随机矩阵并将其转化为行阶梯形矩阵。