Given two N x M matrices. Find a N x M matrix as the sum of given matrices each value at the sum of values of corresponding elements of the given two matrices.

Approach: Below is the idea to solve the problem.

Iterate over every cell of matrix (i, j), add the corresponding values of the two matrices and store in a single matrix i.e. the resultant matrix.

Try It Yourself

Follow the below steps to Implement the idea:

Initialize a resultant matrix res[N][M].
Run a for loop for counter i as each row and in each iteration:
- Run a for loop for counter j as each column and in each iteration:
  - Add values of the two matrices for index i, j and store in res[i][j].
Return res.

Below is the Implementation of above approach.

C++

#include <iostream>
#include <vector>
using namespace std;

void add(vector<vector<int>>& A, vector<vector<int>>& B, 
                                 vector<vector<int>>& C) {
    int n = A.size();
    int m = A[0].size();
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
}

int main() {
    vector<vector<int>> A = { {1, 1, 1},
                              {2, 2, 2},
                              {3, 3, 3},
                              {4, 4, 4} };

    vector<vector<int>> B = { {1, 1, 1},
                              {2, 2, 2},
                              {3, 3, 3},
                              {4, 4, 4} };

    int n = A.size();
    int m = A[0].size();
    vector<vector<int>> C(n, vector<int>(m));
  
    add(A, B, C);

    cout << "Result matrix is:" << endl;
    for (const auto& row : C) {
        for (int val : row) {
            cout << val << " ";
        }
        cout << endl;
    }

    return 0;
}

#include <stdio.h>
#include <stdlib.h>

#define N 4  // Number of rows
#define M 3  // Number of columns

void add(int A[][M], int B[][M], int C[][M]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
}

int main() {
    int A[N][M] = { {1, 1, 1}, {2, 2, 2}, {3, 3, 3}, {4, 4, 4} };
    int B[N][M] = { {1, 1, 1}, {2, 2, 2}, {3, 3, 3}, {4, 4, 4} };
    int C[N][M];

    add(A, B, C);

    printf("Result matrix is:\n");
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            printf("%d ", C[i][j]);
        }
        printf("\n");
    }
    return 0;
}

Java

public class GfG {
    public static void add(int[][] A, int[][] B, int[][] C) {
        int n = A.length;
        int m = A[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                C[i][j] = A[i][j] + B[i][j];
            }
        }
    }

    public static void main(String[] args) {
        int[][] A = { {1, 1, 1}, {2, 2, 2}, {3, 3, 3}, {4, 4, 4} };
        int[][] B = { {1, 1, 1}, {2, 2, 2}, {3, 3, 3}, {4, 4, 4} };
        int[][] C = new int[4][3];
        add(A, B, C);

        System.out.println("Result matrix is:");
        for (int[] row : C) {
            for (int val : row) {
                System.out.print(val + " ");
            }
            System.out.println();
        }
    }
}

Python

def add(A, B):
    n = len(A)
    m = len(A[0])
    C = [[0] * m for _ in range(n)]
    for i in range(n):
        for j in range(m):
            C[i][j] = A[i][j] + B[i][j]
    return C

A = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ]
B = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ]
C = add(A, B)

print("Result matrix is:")
for row in C:
    print(' '.join(map(str, row)))

JavaScript

function add(A, B) {
    let n = A.length;
    let m = A[0].length;
    let C = Array.from({ length: n }, () => Array(m).fill(0));
    for (let i = 0; i < n; i++) {
        for (let j = 0; j < m; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }
    return C;
}

const A = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ];
const B = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ];
const C = add(A, B);

console.log("Result matrix is:");
C.forEach(row => {
    console.log(row.join(' '));
});

PHP

<?php
function add($A, $B) {
    $n = count($A);
    $m = count($A[0]);
    $C = array_fill(0, $n, array_fill(0, $m, 0));
    for ($i = 0; $i < $n; $i++) {
        for ($j = 0; $j < $m; $j++) {
            $C[$i][$j] = $A[$i][$j] + $B[$i][$j];
        }
    }
    return $C;
}

$A = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ];
$B = [ [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4] ];
$C = add($A, $B);

echo "Result matrix is:\n";
foreach ($C as $row) {
    echo implode(' ', $row) . "\n";
}
?>

Output

Result matrix is 
2 2 2 2 
4 4 4 4 
6 6 6 6 
8 8 8 8

Time complexity: O(n x m).
Auxiliary space: O(n x m). since n² extra space has been taken for storing results

The program can be extended for rectangular matrices. The following post can be useful for extending this program.

How to pass a 2D array as a parameter in C?

Program for addition of two matrices

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