Two-dimensional (2D) lists, often referred to as lists of lists, are a way to store tabular data in Python. They are particularly useful for representing matrices, grids, or any other form of nested data structures. Here’s a comprehensive look at 2D lists with various examples to illustrate their creation, access, manipulation, and practical applications.

### Creating a 2D List

You can create a 2D list by nesting lists within a list.

**Example**:

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matrix = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] print(matrix) |

### Accessing Elements

To access elements in a 2D list, you use two indices – the first for the row and the second for the column.

**Example**:

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# Accessing the element on the first row and second column print(matrix[0][1]) # Output: 2 # Accessing the entire second row print(matrix[1]) # Output: [4, 5, 6] |

### Modifying Elements

Similar to accessing elements, you modify them by referring to their row and column indices.

**Example**:

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# Changing the value of an element matrix[0][0] = 10 print(matrix[0]) # Output: [10, 2, 3] |

### Iterating Through a 2D List

You can iterate through each row in a 2D list with a `for`

loop, and nest another `for`

loop to iterate through each column of the current row.

**Example**:

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for row in matrix: for item in row: print(item, end=' ') print() # Creates a new line after each row |

### List Comprehensions with 2D Lists

List comprehensions can also be used to create or modify 2D lists in a concise manner.

**Example: Creating a 2D list using list comprehension**:

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# Create a 3x3 matrix with all values set to 0 matrix = [[0 for _ in range(3)] for _ in range(3)] print(matrix) |

**Example: Flattening a 2D list into a 1D list**:

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flattened = [item for row in matrix for item in row] print(flattened) |

### Practical Application: Matrix Operations

2D lists are often used to perform matrix operations such as addition, multiplication, transposition, etc.

**Example: Matrix Transposition**:

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# Transpose of a matrix transpose = [[matrix[j][i] for j in range(len(matrix))] for i in range(len(matrix[0]))] print(transpose) |

### Working with Rows and Columns

Manipulating rows and columns, such as adding or removing them, involves operations on the outer and inner lists, respectively.

**Example: Adding a row**:

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new_row = [10, 11, 12] matrix.append(new_row) print(matrix) |

**Example: Adding a column**:

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for i in range(len(matrix)): matrix[i].append(i) # Adds the current index as a new column value print(matrix) |

2D lists in Python offer a flexible way to work with complex datasets, allowing for efficient data manipulation and retrieval. Understanding how to effectively create, access, and manipulate these structures is crucial for tasks that involve multi-dimensional data, such as scientific computing, game development, and data analysis.