编写一个矩阵类Matrix，实现矩阵加法，减法，乘法和数乘功能。 本题中数乘用于将矩阵中的每个元素扩大整除倍。 输入： 输入为三个矩阵 每个矩阵输入的第一行为M，N两个整数，表示矩阵的行数和列数 ； 接下来M行为矩阵的内容 。 输出： 矩阵求和、差值和乘积

为了实现这个Matrix类，我们可以首先定义一个内部数据结构来存储矩阵，然后分别添加加法、减法、乘法和数乘的方法。这里是一个简单的Python实现示例：

class Matrix:
    def __init__(self, rows, cols):
        self.rows = rows
        self.cols = cols
        self.data = []

    def input_matrix(self, matrix_string):
        self.data = [[int(num) for num in row.split()] for row in matrix_string.strip().split("\n")]

    def add_matrix(self, other):
        if self.rows != other.rows or self.cols != other.cols:
            raise ValueError("Matrices must have the same dimensions.")
        result = Matrix(self.rows, self.cols)
        result.data = [list(map(sum, zip(a, b))) for a, b in zip(self.data, other.data)]
        return result

    def subtract_matrix(self, other):
        if self.rows != other.rows or self.cols != other.cols:
            raise ValueError("Matrices must have the same dimensions.")
        result = Matrix(self.rows, self.cols)
        result.data = [list(map(lambda x, y: x - y, a, b)) for a, b in zip(self.data, other.data)]
        return result

    def multiply_matrix(self, other):
        if self.cols != other.rows:
            raise ValueError("The number of columns in the first matrix must be equal to the number of rows in the second matrix.")
        result = Matrix(other.rows, self.cols)
        result.data = [[sum(row * col for row in other.data[i]) for col in self.data[j]] for i, j in enumerate(result.data)]
        return result

    def scalar_multiply(self, scalar):
        new_data = [[cell * scalar for cell in row] for row in self.data]
        return Matrix(self.rows, self.cols, new_data)

# 示例：
matrix_a = Matrix(2, 2).input_matrix("1 2\n3 4")
matrix_b = Matrix(2, 2).input_matrix("5 6\n7 8")

matrix_sum = matrix_a.add_matrix(matrix_b)
matrix_diff = matrix_a.subtract_matrix(matrix_b)
matrix_prod = matrix_a.multiply_matrix(matrix_b)
scaled_matrix = matrix_a.scalar_multiply(2)

print("Sum:\n", matrix_sum.data)
print("Difference:\n", matrix_diff.data)
print("Product:\n", matrix_prod.data)
print("Scalar Multiply (2x):\n", scaled_matrix.data)