Write A C++ Program To Add Two Matrix Of Order 4 4

This article provides a clear guide on how to add two 4x4 matrices using a C++ program. You will learn the fundamental concepts of matrix addition and how to implement them effectively in C++.

Problem Statement

The task is to write a C++ program that takes two 4x4 matrices as input, calculates their sum, and then displays the resulting sum matrix. Matrix addition involves adding corresponding elements of two matrices to produce a new matrix of the same dimensions.

Example

Consider two 4x4 matrices, Matrix A and Matrix B. Their sum, Matrix C, is calculated by adding the elements at the same position in A and B.

Matrix A:

1  2  3  4
5  6  7  8
9 10 11 12
13 14 15 16

Matrix B:

16 15 14 13
12 11 10  9
 8  7  6  5
 4  3  2  1

Resulting Sum Matrix (C = A + B):

17 17 17 17
17 17 17 17
17 17 17 17
17 17 17 17

Background & Knowledge Prerequisites

To understand this program, you should have a basic understanding of:

• C++ Syntax: Variables, data types, basic input/output operations.
• Arrays: How to declare and use one-dimensional and multi-dimensional arrays (specifically 2D arrays).
• Loops: for loops for iteration over arrays and performing repetitive tasks.

Use Cases or Case Studies

Matrix addition is a fundamental operation in various fields:

• Computer Graphics: Used in transformations like translation, scaling, and rotation of 2D or 3D objects.
• Physics and Engineering: Solving systems of linear equations, analyzing stress and strain in materials, or modeling complex systems.
• Machine Learning: Part of many algorithms, especially in neural networks where weights and biases are often represented as matrices.
• Image Processing: Used for operations like image blending or applying filters.

Solution Approaches

For adding two matrices, the most direct and common approach involves iterating through each corresponding element of the input matrices and adding them.

Matrix Addition using Nested Loops

This approach uses nested for loops to traverse both matrices simultaneously, adding their elements and storing the result in a third matrix.

One-line summary: Iterate through rows and columns of both input matrices, summing corresponding elements into a result matrix.

Code Example:

// Add Two 4x4 Matrices
#include <iostream> // Required for input/output operations

int main() {
    // Step 1: Declare three 4x4 matrices
    // matrix1 and matrix2 will store the input matrices
    // sumMatrix will store the result of the addition
    int matrix1[4][4];
    int matrix2[4][4];
    int sumMatrix[4][4];

    // Step 2: Get input for the first matrix (matrix1)
    std::cout << "Enter elements for the first 4x4 matrix:" << std::endl;
    for (int i = 0; i < 4; ++i) { // Loop for rows
        for (int j = 0; j < 4; ++j) { // Loop for columns
            std::cout << "Enter element at position [" << i << "][" << j << "]: ";
            std::cin >> matrix1[i][j];
        }
    }

    // Step 3: Get input for the second matrix (matrix2)
    std::cout << "\\nEnter elements for the second 4x4 matrix:" << std::endl;
    for (int i = 0; i < 4; ++i) { // Loop for rows
        for (int j = 0; j < 4; ++j) { // Loop for columns
            std::cout << "Enter element at position [" << i << "][" << j << "]: ";
            std::cin >> matrix2[i][j];
        }
    }

    // Step 4: Perform matrix addition
    // Add corresponding elements of matrix1 and matrix2 and store in sumMatrix
    for (int i = 0; i < 4; ++i) { // Loop for rows
        for (int j = 0; j < 4; ++j) { // Loop for columns
            sumMatrix[i][j] = matrix1[i][j] + matrix2[i][j];
        }
    }

    // Step 5: Display the resulting sum matrix
    std::cout << "\\nResultant Sum Matrix:" << std::endl;
    for (int i = 0; i < 4; ++i) { // Loop for rows
        for (int j = 0; j < 4; ++j) { // Loop for columns
            std::cout << sumMatrix[i][j] << "\\t"; // Print element followed by a tab for formatting
        }
        std::cout << std::endl; // Move to the next line after printing each row
    }

    return 0; // Indicate successful program execution
}

Run

Sample Output:

Enter elements for the first 4x4 matrix:
Enter element at position [0][0]: 1
Enter element at position [0][1]: 2
Enter element at position [0][2]: 3
Enter element at position [0][3]: 4
Enter element at position [1][0]: 5
Enter element at position [1][1]: 6
Enter element at position [1][2]: 7
Enter element at position [1][3]: 8
Enter element at position [2][0]: 9
Enter element at position [2][1]: 10
Enter element at position [2][2]: 11
Enter element at position [2][3]: 12
Enter element at position [3][0]: 13
Enter element at position [3][1]: 14
Enter element at position [3][2]: 15
Enter element at position [3][3]: 16

Enter elements for the second 4x4 matrix:
Enter element at position [0][0]: 16
Enter element at position [0][1]: 15
Enter element at position [0][2]: 14
Enter element at position [0][3]: 13
Enter element at position [1][0]: 12
Enter element at position [1][1]: 11
Enter element at position [1][2]: 10
Enter element at position [1][3]: 9
Enter element at position [2][0]: 8
Enter element at position [2][1]: 7
Enter element at position [2][2]: 6
Enter element at position [2][3]: 5
Enter element at position [3][0]: 4
Enter element at position [3][1]: 3
Enter element at position [3][2]: 2
Enter element at position [3][3]: 1

Resultant Sum Matrix:
17	17	17	17	
17	17	17	17	
17	17	17	17	
17	17	17	17

Stepwise Explanation:

1. Include Header: The iostream header is included for standard input (std::cin) and output (std::cout) operations.
2. Matrix Declaration: Three 2D integer arrays (matrix1, matrix2, sumMatrix) are declared, each with dimensions [4][4] to hold 4x4 matrices.
3. Input for matrix1: Nested for loops iterate from row 0 to 3 and column 0 to 3. Inside the loops, the program prompts the user to enter each element of the first matrix.
4. Input for matrix2: Similar to matrix1, the program takes input for all elements of the second matrix.
5. Matrix Addition: Another set of nested for loops performs the core operation. For each corresponding position [i][j], the element from matrix1 is added to the element from matrix2, and the result is stored in sumMatrix[i][j].
6. Display sumMatrix: The final set of nested for loops iterates through sumMatrix and prints each element. std::cout << "\t"; is used to print a tab for better spacing, and std::cout << std::endl; moves the cursor to the next line after each row is printed.

Conclusion

This article demonstrated a straightforward C++ program to add two 4x4 matrices. By utilizing nested loops and fundamental array concepts, you can efficiently perform matrix addition, a core operation in various computational tasks.

Summary

• Matrix addition involves summing corresponding elements of two matrices of the same dimension.
• 2D arrays in C++ are used to represent matrices.
• Nested for loops are essential for iterating through rows and columns to input data, perform addition, and display results.
• The program structure is clear, separating input, calculation, and output phases.