Matrices (2D Lists)

A matrix is a grid of numbers organized in rows and columns. Think of a spreadsheet, a chess board, or a pixel screen: all are grids. In Python, we represent a matrix as a list of lists

matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

This is a 3×3 matrix (3 rows, 3 columns). Each inner list is a row

To access an element, we use two indexes: matrix[row][column]

print(matrix[0][0])   # 1  (row 0, column 0)
print(matrix[1][2])   # 6  (row 1, column 2)
print(matrix[2][1])   # 8  (row 2, column 1)

To go through every element, we use nested loops

matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

for row in matrix:
    for element in row:
        print(element, end=" ")
    print()

Output

1 2 3
4 5 6
7 8 9

The outer loop goes through each row (which is a list). The inner loop goes through each element in that row. print() at the end starts a new line after each row

If we need the indexes (to know where we are)

matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

for i in range(len(matrix)):
    for j in range(len(matrix[i])):
        print(f"[{i}][{j}] = {matrix[i][j]}")

Common operations on matrices

Sum of all elements

total = 0
for row in matrix:
    for element in row:
        total += element
print(total)

Output 45

Find the maximum

biggest = matrix[0][0]
for row in matrix:
    for element in row:
        if element > biggest:
            biggest = element
print(biggest)

Output 9

A real-life use case: imagine a game map where 0 is empty and 1 is a wall

game_map = [
    [0, 0, 1, 0],
    [0, 1, 0, 0],
    [0, 0, 0, 1],
    [1, 0, 0, 0]
]

walls = 0
for row in game_map:
    for cell in row:
        if cell == 1:
            walls += 1
print(f"Number of walls: {walls}")

Output Number of walls: 4

Mission: Sensor Grid

The station's hull sensors report their readings as a 4×4 grid (a list of lists named grid, already on the right). Mission Control wants a quick summary of the grid.

Using nested loops, print:

The sum of each row, one per line, labelled Row 1: , Row 2: , and so on (rows numbered from 1).
Max: followed by the single highest reading anywhere in the grid.
Above 7: followed by how many readings are strictly greater than 7.

Output

Row 1: 22
Row 2: 26
Row 3: 15
Row 4: 37
Max: 10
Above 7: 7