Posted on by Kalkicode
Code Matrix

Matrix addition is a fundamental operation in linear algebra, which is widely used in various fields including mathematics, engineering, computer graphics, and data analysis. It involves adding corresponding elements of two matrices to produce a new matrix. This operation is based on the principle that the matrices being added must have the same dimensions.

Problem Statement

Given two matrices A and B of size ROW x COL, the task is to perform matrix addition and obtain a new matrix C, where each element c[i][j] is the sum of the corresponding elements from matrices A and B, i.e., c[i][j] = a[i][j] + b[i][j].

Description

Matrix addition is an important operation that combines the elements of two matrices to create a third matrix. Let's take a closer look at how matrix addition works with an example.

Consider two matrices: Matrix A:

``````1  2  3
-6  1  2
5  4  3``````

Matrix B:

``````3  1  4
1  7  3
2  2  2``````

``````(1+3)  (2+1)  (3+4)
(-6+1) (1+7)  (2+3)
(5+2)  (4+2)  (3+2)``````

This results in the following matrix:

``````4  3  7
-5  8  5
7  6  5``````

Idea to Solve the Problem

The problem can be solved by following these steps:

1. Define two matrices A and B with the same dimensions (ROW x COL).
2. Iterate through each element of the matrices and calculate the sum of the corresponding elements.
3. Store the sum in a new matrix C of the same dimensions.
4. Display the matrices A, B, and C to showcase the inputs and the result of the addition.

Pseudocode

Here's the pseudocode to perform matrix addition:

``````function matrixAddition(matrix1, matrix2):
initialize result matrix of the same dimensions as matrix1 and matrix2

for i from 0 to ROW - 1:
for j from 0 to COL - 1:
result[i][j] = matrix1[i][j] + matrix2[i][j]

display "Matrix A:"
display matrix1
display "Matrix B:"
display matrix2
display "Matrix A + Matrix B:"
display result``````

Algorithm Explanation

1. The function `matrixAddition` takes two matrices `matrix1` and `matrix2` as input and initializes a new matrix `result` of the same dimensions.
2. It then iterates through each element using two nested loops, where `i` represents the row index and `j` represents the column index.
3. For each element, it calculates the sum of the corresponding elements from `matrix1` and `matrix2` and stores it in the corresponding position of the `result` matrix.
4. After calculating the entire `result` matrix, the function displays the original matrices `matrix1` and `matrix2`, and then displays the result matrix `result`.

Code Solution

``````/*
C Program
*/
#include <stdio.h>

#define ROW 3
#define COL 3

//Display the element of given 2d matrix
void show_data(int matrix[][COL]) {

printf("-----------------\n");

for (int i = 0; i < ROW; ++i) {

for (int j = 0; j < COL; ++j) {

printf("%4d", matrix[i][j]);
}

printf("\n");
}

printf("\n");
}
{

//This matrix are store the result of addition
int result[ROW][COL];

for (int i = 0; i < ROW; ++i) {

for (int j = 0; j < COL; ++j) {

//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j];

}
}
//Display Matrix Elements
printf("  Matrix A\n");
//print element of matrix1
show_data(matrix1);

printf("\n  Matrix B\n");
//print element of matrix1
show_data(matrix2);

printf("\n (Matrix A) + \n (Matrix B)\n");
//Display resultant matrix
show_data(result);

}
int main() {
//Define matrix 1
int matrix1[ROW][COL] = {
{
1, 2, 3
},

{
-6, 1, 2
},
{
5, 4, 3
}
};

//Define matrix 2
int matrix2[ROW][COL] = {
{
3, 1, 4
},
{
1, 7, 3
},
{
2, 2, 2
}
};

return 0;
}```
```

Output

``````  Matrix A
-----------------
1   2   3
-6   1   2
5   4   3

Matrix B
-----------------
3   1   4
1   7   3
2   2   2

(Matrix A) +
(Matrix B)
-----------------
4   3   7
-5   8   5
7   6   5
``````
``````/*
C++ Program
*/
#include<iostream>
using namespace std;
#define ROW 3
#define COL 3
class MyMatrix {
public:

//Display the element of given 2d matrix
void show_data(int matrix[ROW][COL]) {
cout << "-----------------\n";
//Assume  N x N Matrix size
for (int i = 0; i < ROW; ++i) {
for (int j = 0; j < COL; ++j) {
cout << " " << matrix[i][j];
}
cout << "\n";
}
cout << "\n";
}
void addition(int matrix1[ROW][COL], int matrix2[ROW][COL]) {
//Assume both matrix are equal size
//Assume  N x N Matrix size

//This matrix are store the result of addition
int result[ROW][COL];
for (int i = 0; i < ROW; ++i) {
for (int j = 0; j < COL; ++j) {
//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j];
}
}
cout << " Matrix A\n";
//print element of matrix1
this->show_data(matrix1);
cout << "\n Matrix B\n";
//print element of matrix1
this->show_data(matrix2);
cout << "\n (Matrix A) + \n (Matrix B)\n";
//Display resultant matrix
this->show_data(result);
}
};
int main() {
MyMatrix obj;
//Define matrix 1
int matrix1[ROW][COL] = {
{
1,
2,
3
},
{
-6,
1,
2
},
{
5,
4,
3
}
};
//Define matrix 2
int matrix2[ROW][COL] = {
{
3,
1,
4
},
{
1,
7,
3
},
{
2,
2,
2
}
};
return 0;
}```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5
``````
``````/*
Java Program
*/
public class MyMatrix {

//Display the element of given 2d matrix
public void show_data(int [][]matrix) {

System.out.print("-----------------\n");

//Assume  N x N Matrix size
int row = matrix.length;

int col = matrix[0].length;

for (int i = 0; i < row; ++i) {

for (int j = 0; j < col; ++j) {

System.out.print("  "+ matrix[i][j]);
}

System.out.print("\n");
}

System.out.print("\n");
}
{
//Assume both matrix are equal size
//Assume  N x N Matrix size
int row = matrix1.length;

int col = matrix1[0].length;

//This matrix are store the result of addition
int [][]result = new int[row][col];

for (int i = 0; i < row; ++i) {

for (int j = 0; j < col; ++j) {

//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j];

}
}
System.out.print("  Matrix A\n");
//print element of matrix1
show_data(matrix1);

System.out.print("\n  Matrix B\n");
//print element of matrix1
show_data(matrix2);

System.out.print("\n (Matrix A) + \n (Matrix B)\n");
//Display resultant matrix
show_data(result);

}

public static void main(String[] args) {

MyMatrix obj = new MyMatrix();
//Define matrix 1
int [][]matrix1 = {
{
1, 2, 3
},

{
-6, 1, 2
},
{
5, 4, 3
}
};

//Define matrix 2
int [][]matrix2 = {
{
3, 1, 4
},
{
1, 7, 3
},
{
2, 2, 2
}
};

}
}```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5
``````
``````/*
C# Program
*/
using System;
public class MyMatrix {

//Display the element of given 2d matrix
public void show_data(int[,] matrix) {

Console.Write("-----------------\n");

//Assume  N x N Matrix size
int row = matrix.GetLength(0);

int col = matrix.GetLength(1);

for (int i = 0; i < row; ++i) {

for (int j = 0; j < col; ++j) {

Console.Write("  " + matrix[i,j]);
}

Console.Write("\n");
}

Console.Write("\n");
}
public void addition(int[,] matrix1, int[,] matrix2) {
//Assume both matrix are equal size
//Assume  N x N Matrix size
int row = matrix1.GetLength(0);

int col = matrix1.GetLength(1);

//This matrix are store the result of addition
int[,] result = new int[row,col];

for (int i = 0; i < row; ++i) {

for (int j = 0; j < col; ++j) {

//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i,j] = matrix1[i,j] + matrix2[i,j];

}
}
Console.Write("  Matrix A\n");
//print element of matrix1
show_data(matrix1);

Console.Write("\n  Matrix B\n");
//print element of matrix1
show_data(matrix2);

Console.Write("\n (Matrix A) + \n (Matrix B)\n");
//Display resultant matrix
show_data(result);

}

public static void Main(String[] args) {

MyMatrix obj = new MyMatrix();
//Define matrix 1
int[,] matrix1 = {
{
1,
2,
3
},

{
-6,
1,
2
},
{
5,
4,
3
}
};

//Define matrix 2
int[,] matrix2 = {
{
3,
1,
4
},
{
1,
7,
3
},
{
2,
2,
2
}
};

}
}```
```

Output

``````  Matrix A
-----------------
1  2  3
-6  1  2
5  4  3

Matrix B
-----------------
3  1  4
1  7  3
2  2  2

(Matrix A) +
(Matrix B)
-----------------
4  3  7
-5  8  5
7  6  5
``````
``````<?php
/*
Php Program
*/
class MyMatrix {
//Display the element of given 2d matrix

public 	function show_data(\$matrix) {
echo("-----------------\n");
//Assume  N x N Matrix size
\$row = count(\$matrix);
\$col = count(\$matrix[0]);
for (\$i = 0; \$i < \$row; ++\$i) {
for (\$j = 0; \$j < \$col; ++\$j) {
echo(" ". \$matrix[\$i][\$j]);
}
echo("\n");
}
echo("\n");
}
//Assume both matrix are equal size
//Assume  N x N Matrix size
\$row = count(\$matrix1);
\$col = count(\$matrix1[0]);
//This matrix are store the result of addition
\$result = array_fill(0, \$row,array_fill(0,\$row,0));
for (\$i = 0; \$i < \$row; ++\$i) {
for (\$j = 0; \$j < \$col; ++\$j) {
//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
\$result[\$i][\$j] = \$matrix1[\$i][\$j] + \$matrix2[\$i][\$j];
}
}
echo(" Matrix A\n");
//print element of matrix1
\$this->show_data(\$matrix1);
echo("\n Matrix B\n");
//print element of matrix1
\$this->show_data(\$matrix2);
echo("\n (Matrix A) + \n (Matrix B)\n");
//Display resultant matrix
\$this->show_data(\$result);
}
};

function main() {
\$obj = new MyMatrix();
//Define matrix 1
\$matrix1 = array(array(1, 2, 3), array(-6, 1, 2), array(5, 4, 3));
//Define matrix 2
\$matrix2 = array(array(3, 1, 4), array(1, 7, 3), array(2, 2, 2));
}
main();```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5
``````
``````/*
Node Js Program
*/
class MyMatrix {
//Display the element of given 2d matrix
show_data(matrix) {
process.stdout.write("-----------------\n");
//Assume  N x N Matrix size
var row = matrix.length;
var col = matrix[0].length;
for (var i = 0; i < row; ++i) {
for (var j = 0; j < col; ++j) {
process.stdout.write(" " + matrix[i][j]);
}
process.stdout.write("\n");
}
process.stdout.write("\n");
}
//Assume both matrix are equal size
//Assume  N x N Matrix size
var row = matrix1.length;
var col = matrix1[0].length;
//This matrix are store the result of addition
var result = Array(row).fill(0).map(() => new Array(col).fill(0));
for (var i = 0; i < row; ++i) {
for (var j = 0; j < col; ++j) {
//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j];
}
}
process.stdout.write(" Matrix A\n");
//print element of matrix1
this.show_data(matrix1);
process.stdout.write("\n Matrix B\n");
//print element of matrix1
this.show_data(matrix2);
process.stdout.write("\n (Matrix A) + \n (Matrix B)\n");
//Display resultant matrix
this.show_data(result);
}
}

function main(args) {
var obj = new MyMatrix();
//Define matrix 1
var matrix1 = [
[1, 2, 3],
[-6, 1, 2],
[5, 4, 3]
];
//Define matrix 2
var matrix2 = [
[3, 1, 4],
[1, 7, 3],
[2, 2, 2]
];
}
main();```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5
``````
``````# Python 3 Program

class MyMatrix :
# Display the element of given 2d matrix
def show_data(self, matrix) :
print("-----------------")
row = len(matrix)
col = len(matrix[0])
i = 0
while (i < row) :
j = 0
while (j < col) :
print(" ", matrix[i][j],end="")
j += 1

print(end="\n")
i += 1

print("\n")

# Assume both matrix are equal size
# Assume  N x N Matrix size
row = len(matrix1)
col = len(matrix1[0])
result = [[0 for i in range(col)] for j in range(row)]
i = 0
while (i < row) :
j = 0
while (j < col) :
# Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j]
j += 1

i += 1

print(" Matrix A")
self.show_data(matrix1)
print(" Matrix B")
self.show_data(matrix2)
print(" (Matrix A) + \n (Matrix B)")
self.show_data(result)

def main() :
obj = MyMatrix()
matrix1 = [
[1, 2, 3],
[-6, 1, 2],
[5, 4, 3]
]
matrix2 = [
[3, 1, 4],
[1, 7, 3],
[2, 2, 2]
]

if __name__ == "__main__":
main()```
```

Output

`````` Matrix A
-----------------
1  2  3
-6  1  2
5  4  3

Matrix B
-----------------
3  1  4
1  7  3
2  2  2

(Matrix A) +
(Matrix B)
-----------------
4  3  7
-5  8  5
7  6  5``````
``````# Ruby Program
class MyMatrix
# Display the element of given 2d matrix
def show_data(matrix)
print("-----------------\n")
row = matrix.length
col = matrix[0].length
i = 0
while (i < row)
j = 0
while (j < col)
print(" ", matrix[i][j])
j += 1
end
print("\n")
i += 1
end
print("\n")
end
# Assume both matrix are equal size
# Assume  N x N Matrix size
row = matrix1.length
col = matrix1[0].length
result = Array.new(row){ Array.new(col, 0) }
i = 0
while (i < row)
j = 0
while (j < col)
# Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j]
j += 1
end
i += 1
end
print(" Matrix A\n")
self.show_data(matrix1)
print("\n Matrix B\n")
self.show_data(matrix2)
print("\n (Matrix A) + \n (Matrix B)\n")
self.show_data(result)
end
end
def main()
obj = MyMatrix.new()
matrix1 = [
[1, 2, 3],
[-6, 1, 2],
[5, 4, 3]
]
matrix2 = [
[3, 1, 4],
[1, 7, 3],
[2, 2, 2]
]
end
main()```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5

``````
``````/*
Scala Program
*/
class MyMatrix {
//Display the element of given 2d matrix
def show_data(matrix: Array[Array[Int]]): Unit = {
print("-----------------\n");
var row: Int = matrix.length;
var col: Int = matrix(0).length;
var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
print(" " + matrix(i)(j));
j += 1;
}
print("\n");
i += 1;
}
print("\n");
}
def addition(matrix1: Array[Array[Int]], matrix2: Array[Array[Int]]): Unit = {
//Assume both matrix are equal size
//Assume  N x N Matrix size
var row: Int = matrix1.length;
var col: Int = matrix1(0).length;
var result: Array[Array[Int]] = Array.fill[Int](row,col)(0);
var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result(i)(j) = matrix1(i)(j) + matrix2(i)(j);
j += 1;
}
i += 1;
}
print(" Matrix A\n");
this.show_data(matrix1);
print("\n Matrix B\n");
this.show_data(matrix2);
print("\n (Matrix A) + \n (Matrix B)\n");
this.show_data(result);
}
}
object Main {
def main(args: Array[String]): Unit = {
var obj: MyMatrix = new MyMatrix();
var matrix1: Array[Array[Int]] = Array(
Array(1, 2, 3),
Array(-6, 1, 2),
Array(5, 4, 3));
var matrix2: Array[Array[Int]] = Array(
Array(3, 1, 4),
Array(1, 7, 3),
Array(2, 2, 2));
}
}```
```

Output

`````` Matrix A
-----------------
1 2 3
-6 1 2
5 4 3

Matrix B
-----------------
3 1 4
1 7 3
2 2 2

(Matrix A) +
(Matrix B)
-----------------
4 3 7
-5 8 5
7 6 5
``````
``````/*
Swift 4 Program
*/
class MyMatrix {
//Display the element of given 2d matrix
func show_data(_ matrix: [
[Int]
]) {
print("-----------------");
let row: Int = matrix.count;
let col: Int = matrix[0].count;
var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
print(" ", matrix[i][j],terminator:"");
j += 1;
}
print(terminator:"\n");
i += 1;
}
print("\n");
}
[Int]
], _ matrix2: [
[Int]
]) {
//Assume both matrix are equal size
//Assume  N x N Matrix size
let row: Int = matrix1.count;
let col: Int = matrix1[0].count;
var result: [[Int]] = Array(repeating : Array( repeating:0 , count:col) ,  count:row);

var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
//Add matrix A [i] row and [j] columns to the Matrix B [j] columns and [i] rows
result[i][j] = matrix1[i][j] + matrix2[i][j];
j += 1;
}
i += 1;
}
print(" Matrix A");
self.show_data(matrix1);
print("\n Matrix B");
self.show_data(matrix2);
print("\n (Matrix A) + \n (Matrix B)");
self.show_data(result);
}
}
func main() {
let obj: MyMatrix = MyMatrix();
let matrix1: [
[Int]
] = [
[1, 2, 3],
[-6, 1, 2],
[5, 4, 3]
];
let matrix2: [
[Int]
] = [
[3, 1, 4],
[1, 7, 3],
[2, 2, 2]
];
}
main();```
```

Output

`````` Matrix A
-----------------
1  2  3
-6  1  2
5  4  3

Matrix B
-----------------
3  1  4
1  7  3
2  2  2

(Matrix A) +
(Matrix B)
-----------------
4  3  7
-5  8  5
7  6  5

``````

Time Complexity

The time complexity of this code is determined by the nested loops used to iterate through the matrices. Since the matrices have dimensions ROW x COL, there are `ROW * COL` elements to process.

Therefore, the time complexity is O(ROW * COL), where ROW and COL are the number of rows and columns in the matrices, respectively.

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