以下是一个示例解决方案，使用Python编程语言：

def average_rows_and_columns(matrix):
    num_rows = len(matrix)
    num_cols = len(matrix[0])
    
    row_averages = []
    for row in matrix:
        row_sum = sum(row)
        row_avg = row_sum / num_cols
        row_averages.append(row_avg)
    
    col_averages = []
    for col in range(num_cols):
        col_sum = sum(matrix[row][col] for row in range(num_rows))
        col_avg = col_sum / num_rows
        col_averages.append(col_avg)
    
    return row_averages, col_averages

# 示例用法
matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]
row_averages, col_averages = average_rows_and_columns(matrix)
print("Row averages:", row_averages)
print("Column averages:", col_averages)

输出结果：

Row averages: [2.0, 5.0, 8.0]
Column averages: [4.0, 5.0, 6.0]

这个示例中，我们定义了一个名为average_rows_and_columns的函数，它接受一个二维矩阵作为输入，并返回按行和列求得的平均值列表。首先，我们获取矩阵的行数和列数。然后，我们使用两个循环分别计算每一行和每一列的和，并计算平均值。最后，我们将这些平均值存储在row_averages和col_averages列表中，并将它们作为结果返回。