This virtual lab on 2D Matrices is designed for undergraduate students. It aims to simplify the understanding of two-dimensional matrix by combining theory, visual aids, and interactive coding tools. The lab offers hands-on practice with matrix operations such as creation, traversal, and manipulation.
Aim
Theory & Applications
A matrix is a structured rectangular array comprising numbers, symbols, or expressions organized into rows and columns. Matrices are foundational in subjects like mathematics, computer science, engineering, physics, and data science. A 2D matrix (two-dimensional matrix) is a grid of elements arranged in horizontal rows and vertical columns. Each element is identified by its position, given by a specific row and column index.
Example:
A =
[1 2 3]
[4 5 6]
[7 8 9]
- Rows: Horizontal lines (e.g., [1, 2, 3] is the first row)
- Columns: Vertical lines (e.g., [1, 4, 7] is the first column)
- Elements: Individual values in the matrix (e.g., 5 is located at row 2, column 2)
Types of 2D Matrices
- Square Matrix: Same number of rows and columns (e.g., 3×3)
- Rectangular Matrix: Different number of rows and columns (e.g., 2×4)
- Identity Matrix: Diagonal elements are 1; all other elements are 0
- Zero Matrix: All elements are 0
- Sparse Matrix: Contains mostly zeroes
Applications
2D matrices play a crucial role across various domains:
- Computer Graphics: Used for image rendering, transformations, and geometric modeling.
- Scientific Computing: Essential for solving complex simulations and mathematical computations.
- Machine Learning & Data Science: Represent datasets, perform matrix operations, and power neural networks.
- Cryptography: Employed in encoding and decoding algorithms to secure information.
- Game Development: Used in pathfinding, map grids, and collision detection.
- Network Theory: Represent graphs and connections using adjacency matrices.
Procedure
Step 1 – Create the Matrix:
- Name the function
create_matrix(m, n), where: mis the number of rowsnis the number of columns- Ask the user to enter
m × nvalues one by one - Return the created matrix
Step 2 – Traverse the Matrix:
- Name the function
traverse_matrix(matrix, r, c), where: matrixis the matrix to traverseris the row indexcis the column index- Check if the index is valid by comparing
randcwith matrix dimensions - If valid, print the value at
matrix[r][c] - If invalid, print
"Invalid index!"
Step 3 – Manipulate the Matrix:
- Name the function
manipulate_matrix(matrix, r, c, new_value), where: matrixis the matrix to manipulateris the row indexcis the column indexnew_valueis the new value to assign- Check if the index is valid
- If valid, update
matrix[r][c]withnew_valueand print a confirmation message - If invalid, print
"Invalid index!"
Final Output:
- First, display the entire matrix after creation
- Then, traverse and display the value at the specified index
- Next, manipulate the matrix and show the updated matrix
Code
Example programs
// C++ Code Example
#include <iostream>
#include <vector>
using namespace std;
// Step 1: Create the matrix
vector<vector<int>> createMatrix(int m, int n) {
vector<vector<int>> matrix(m, vector<int>(n));
cout << "Enter " << m * n << " elements one by one:" << endl;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
cin >> matrix[i][j];
}
}
return matrix;
}
// Step 2: Traverse the matrix by index
void traverseMatrix(const vector<vector<int>>& matrix, int r, int c) {
if (r < 0 || r >= matrix.size() || c < 0 || c >= matrix[0].size()) {
cout << "Invalid index!" << endl;
} else {
cout << "Value at index [" << r << "][" << c << "] is " << matrix[r][c] << endl;
}
}
// Step 3: Manipulate the matrix at a given index
void manipulateMatrix(vector<vector<int>>& matrix, int r, int c, int newValue) {
if (r < 0 || r >= matrix.size() || c < 0 || c >= matrix[0].size()) {
cout << "Invalid index!" << endl;
} else {
matrix[r][c] = newValue;
cout << "Updated value at index [" << r << "][" << c << "] to " << newValue << endl;
}
}
int main() {
int m, n;
cout << "Enter number of rows: ";
cin >> m;
cout << "Enter number of columns: ";
cin >> n;
vector<vector<int>> mat = createMatrix(m, n);
cout << "\nMatrix:" << endl;
for (const auto& row : mat) {
for (int val : row) {
cout << val << " ";
}
cout << endl;
}
// Traversal
int r, c;
cout << "\nEnter row index to traverse: ";
cin >> r;
cout << "Enter column index to traverse: ";
cin >> c;
traverseMatrix(mat, r, c);
// Manipulation
cout << "\nEnter row index to update: ";
cin >> r;
cout << "Enter column index to update: ";
cin >> c;
int newValue;
cout << "Enter new value: ";
cin >> newValue;
manipulateMatrix(mat, r, c, newValue);
cout << "\nUpdated Matrix:" << endl;
for (const auto& row : mat) {
for (int val : row) {
cout << val << " ";
}
cout << endl;
}
return 0;
}
# Python Code Example
# Step 1: Create the matrix
def create_matrix(m,n):
M = []
for i in range(m):
row = []
for j in range(n):
val = input(f"Element at ({i+1},{j+1}): ")
row.append(val)
M.append(row)
return M
# Step 2: Traverse the matrix by index
def traverse_matrix(matrix, r, c):
if r < 0 or r >= len(matrix) or c < 0 or c >= len(matrix[0]):
print("Invalid index!")
else:
print(f"Value at index [{r}][{c}] is {matrix[r][c]}")
# Step 3: Manipulate the matrix at a given index
def manipulate_matrix(matrix, r, c, new_value):
if r < 0 or r >= len(matrix) or c < 0 or c >= len(matrix[0]):
print("Invalid index!")
else:
matrix[r][c] = new_value
print(f"Updated value at index [{r}][{c}] to {new_value}")
# Example usage:
m = int(input("Enter number of rows: "))
n = int(input("Enter number of columns: "))
mat = create_matrix(m, n)
print("\nMatrix:")
for row in mat:
print(row)
# Traversal
r = int(input("\nEnter row index to traverse: "))
c = int(input("Enter column index to traverse: "))
traverse_matrix(mat, r, c)
# Manipulation
r = int(input("\nEnter row index to manipulate: "))
c = int(input("Enter column index to manipulate: "))
new_value = int(input("Enter new value: "))
manipulate_matrix(mat, r, c, new_value)
print("\nUpdated Matrix:")
for row in mat:
print(row)
Matrix Learning Journey
Welcome! In this lab, we will learn matrices step by step:
1. Creation → 2. Traversal → 3. Manipulation
Result
This virtual lab provides hands-on experience with 2D matrix generation. It enables users to explore different methods, implement code in languages like python and c++ , and visualize the results for better comprehension. By providing quizzes and step-by-step visualizations, it helps learners strengthen both conceptual clarity and problem-solving skills. This virtual setup ensures accessible, self-paced learning, especially for those without access to physical lab resources.
Quiz
References
-
Python Matrix Basics
- Python Lists - W3Schools
- Matrix Applications - Linear Algebra
Team & Tools
Students
Mentor
- Ms. Shiva Saini
Tools Used
- Vanilla HTML, CSS, JS - for creating the web page