定义3*3矩阵类Matrix，在其中重载运算符“+” “-” “*”实现矩阵的基本运算

在定义一个3x3矩阵类`Matrix`，首先我们需要考虑包含三个二维数组来表示矩阵的行和列，以及一些基本属性如元素值、维度等。为了能重载运算符`+`（加法）、`-`（减法）和`*`（乘法），我们需要覆盖这些操作符的函数，让它们能够对矩阵元素进行对应位置的加减乘计算。 以下是一个简单的Python示例： ```python class Matrix3x3: def __init__(self, elements): self.rows = [list(row) for row in elements] def __add__(self, other): if isinstance(other, Matrix3x3) and len(self.rows) == len(other.rows) and len(self.rows[0]) == len(other.rows[0]): result = [[self[i][j] + other[i][j] for j in range(len(self.rows[0]))] for i in range(len(self.rows))] return Matrix3x3(result) else: raise ValueError("Cannot add matrices of different dimensions") def __sub__(self, other): # 类似于__add__方法，只需将加法变为减法即可 if isinstance(other, Matrix3x3) and ...: return Matrix3x3([self[i][j] - other[i][j] for j in range(len(self.rows[0])) for i in range(len(self.rows))]) def __mul__(self, other): if isinstance(other, (int, float)) or (isinstance(other, Matrix3x3) and len(self.rows) == other.cols): # 检查是否可以进行矩阵乘法 result = [[sum(self[i][k] * other[j][k] for k in range(len(self.rows[0]))) for j in range(len(other.rows))] for i in range(len(self.rows))] return Matrix3x3(result) else: raise ValueError("Invalid operation: cannot multiply matrix with incompatible dimension.") # 示例用法 matrix1 = Matrix3x3([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) matrix2 = Matrix3x3([[9, 8, 7], [6, 5, 4], [3, 2, 1]]) result_add = matrix1 + matrix2 result_sub = matrix1 - matrix2 result_mul = matrix1 * 2 print("Matrix addition:", result_add) print("Matrix subtraction:", result_sub) print("Scalar multiplication:", result_mul) ```