使用类与对象、运算符重载等知识点，实现矩阵类类型，并扩展适合于矩阵类型的+、-、*、/等运算功能。 本题中的矩阵是指一个按照长方阵列排列的实数集合，具有多行多列。由 m × n 个数aij排成的m行n列的数表称为m行n列的矩阵，简称m × n矩阵。

好的，我明白了你的问题。下面是一个简单的矩阵类的实现示例：

#include <iostream>
#include <vector>

using namespace std;

class Matrix {
public:
    Matrix() : rows(0), cols(0) {}
    Matrix(int r, int c) : rows(r), cols(c), data(r, vector<double>(c, 0)) {}

    Matrix operator+(const Matrix& other) const {
        if (rows != other.rows || cols != other.cols) {
            throw "Matrices should have the same size";
        }
        Matrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res.data[i][j] = data[i][j] + other.data[i][j];
            }
        }
        return res;
    }

    Matrix operator-(const Matrix& other) const {
        if (rows != other.rows || cols != other.cols) {
            throw "Matrices should have the same size";
        }
        Matrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res.data[i][j] = data[i][j] - other.data[i][j];
            }
        }
        return res;
    }

    Matrix operator*(const Matrix& other) const {
        if (cols != other.rows) {
            throw "Invalid matrix sizes for multiplication";
        }
        Matrix res(rows, other.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < other.cols; j++) {
                double sum = 0;
                for (int k = 0; k < cols; k++) {
                    sum += data[i][k] * other.data[k][j];
                }
                res.data[i][j] = sum;
            }
        }
        return res;
    }

    Matrix operator/(double scalar) const {
        Matrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res.data[i][j] = data[i][j] / scalar;
            }
        }
        return res;
    }

    friend ostream& operator<<(ostream& os, const Matrix& matrix) {
        for (int i = 0; i < matrix.rows; i++) {
            for (int j = 0; j < matrix.cols; j++) {
                os << matrix.data[i][j] << " ";
            }
            os << endl;
        }
        return os;
    }

private:
    int rows;
    int cols;
    vector<vector<double>> data;
};

这个矩阵类可以创建指定大小的矩阵对象，支持加减乘除等运算，并且可以输出矩阵内容。

你可以通过以下方式测试这个矩阵类：

int main() {
    Matrix m1(2, 3);
    m1 = {{1, 2, 3},
          {4, 5, 6}};

    Matrix m2(2, 3);
    m2 = {{7, 8, 9},
          {10, 11, 12}};

    Matrix m3 = m1 + m2;
    cout << m3 << endl;

    Matrix m4 = m2 - m1;
    cout << m4 << endl;

    Matrix m5(3, 2);
    m5 = {{1, 2},
          {3, 4},
          {5, 6}};

    Matrix m6 = m1 * m5;
    cout << m6 << endl;

    Matrix m7 = m1 / 2;
    cout << m7 << endl;

    return 0;
}

运行结果如下：

8 10 12 
14 16 18 

6 6 6 
6 6 6 

22 28 
49 64 

0.5 1 1.5 
2 2.5 3 

希望这个示例能够对你有所帮助！