**C programs to add two matrices** have been shown here. Two matrices $[A]_{m \times n}$ and $[B]_{p \times q}$ are considered for addition if the number of rows and columns are same in both of the matrices i.e. $m = p$ and $n = q$.

Algorithm, pseudocode and time complexity of the program have also been shown.

## 1. Algorithm for matrix addition

1. Take two matrice $A_{m\times n}$ and $B_{p\times q}$

2. Check if $m=p$ and $n=q$

3. If step [2] is false then print "Addition not possible" and exit program

4. If step [2] is true, then

5. Add each corresponding elements of $A$ and $B$

6. Print the result and exit program

## 2. Pseudocode for matrix addition

**Input**: Two matrices $A_{m\times n}$ and $B_{p\times q}$

**Output**: $A + B$

1. **Procedure** matrixAddition($A_{m\times n}$, $B_{p\times q}$):

2. **If** $m==p$ and $n==q$:

3. **Repeat** for each $i \in m$ and $j \in n$

4.

5. **Return** $C$

6. **Else:**

7. ** Return ***Addition Not Pssible*

8. **End Procedure**

## 3. Time Complexity for matrix addition

**Time Complexity:** **O($mn$)**

Where $m$ is the number of rows and $n$ is the number of columns in the matrices.

## 4. C Program for matrix addition

/********************************** alphabetacoder.com C Program for Matrix Addition ***********************************/ #include <stdio.h> int main() { // declare variables int m, n, p, q, i, j; int A[10][10] = {0}, B[10][10] = {0}; //take input of the order of first matrix printf("Enter the number of row and column of first matrix = "); scanf("%d%d", & m, & n); //take input of the first matrix printf("Enter the first matrix of order %d x %d = \n", m, n); for (i = 0; i < m; i++) for (j = 0; j < n; j++) scanf("%d", & A[i][j]); //take input of the order of second matrix printf("Enter the number of row and column of second matrix = "); scanf("%d%d", & p, & q); //take input of the first matrix printf("Enter the second matrix of order %d x %d = \n", p, q); for (i = 0; i < p; i++) for (j = 0; j < q; j++) scanf("%d", & B[i][j]); // check if order of matrices are same // if not then addition of two matrices is not possible if (m != p || n != q) printf("\nMatrices are of different order,hence addition is not possible"); else { //add each corresponding elements // and element wise print the result printf("The resultant matrix after addition:\n"); for (i = 0; i < m; i++) { for (j = 0; j < n; j++) printf("%d ", A[i][j] + B[i][j]); printf("\n"); } } return 0; }

Output

**Case 1:**

Enter the number of row and column of first matrix = 3 3

Enter the first matrix of order 3 x 3 =

3 5 7

4 5 9

0 1 1

Enter the number of row and column of second matrix = 3 3

Enter the second matrix of order 3 x 3 =

9 4 5

3 7 8

1 2 3

The resultant matrix after addition:=

12 9 12

7 12 17

1 3 4

**Case 2:**

Enter the number of row and column of first matrix = 3 3

Enter the first matrix of order 3 x 3 =

3 5 7

4 5 9

0 1 1

Enter the number of row and column of second matrix = 2 3

Enter the second matrix of order 2 x 3 =

9 4 5

3 7 8

Matrices are of different order,hence addition is not possible

## 5. C Program for matrix addition using recursion

/********************************************** Alphabetacoder.com C program for matrix addition using recursion ***********************************************/ #include <stdio.h> #define MAXSIZE 10 // Declare a recursive function to add two matrices // This function takes two matices (A and B), Sizes of both matrices (m, n) // and index of current row & column as parameters // Elementwise addition is stored in B int add_matrices(int A[][MAXSIZE], int B[][MAXSIZE], int m, int n, int row, int col) { // check if all columns are traversed // if yes the set col = 0 and increment row if (col >= n) { row++; col = 0; } // check if all rows are traversed if (row >= m) return 1; // Add corresponding elements // Store the result in matrix B B[row][col] = A[row][col] + B[row][col]; // return the call of recursive function // to consider the next element return add_matrices(A, B, m, n, row, col + 1); } int main() { // declare variables int m, n, p, q, flag = 0, i, j; int A[MAXSIZE][MAXSIZE] = {0}, B[MAXSIZE][MAXSIZE] = {0}; //take input of the order of first matrix printf("Enter the number of row and column of first matrix = "); scanf("%d%d", & m, & n); //take input of the first matrix printf("Enter the first matrix of order %d x %d = \n", m, n); for (i = 0; i < m; i++) { for (j = 0; j < n; j++) { scanf("%d", & A[i][j]); } } //take input of the order of second matrix printf("Enter the number of row and column of second matrix = "); scanf("%d%d", & p, & q); //take input of the first matrix printf("Enter the second matrix of order %d x %d = \n", p, q); for (i = 0; i < p; i++) { for (j = 0; j < q; j++) { scanf("%d", & B[i][j]); } } // check if order of matrices are same // if same then add two matrices if (m != p || n != q) { printf("\nMatrices are of different order, hence addition is not possible"); flag = 1; } else { // Add two matrices by calling a recursive function add_matrices(A, B, m, n, 0, 0); // Display the B matrix as result printf("The resultant matrix after addition:\n"); for (i = 0; i < p; i++) { for (j = 0; j < q; j++) { printf("%d ", B[i][j]); } // new line printf("\n"); } } return 0; }

Output

**Case 1:**

Enter the number of row and column of first matrix = 3 3

Enter the first matrix of order 3 x 3 =

1 2 3

4 5 6

3 4 2

Enter the number of row and column of second matrix = 3 3

Enter the second matrix of order 3 x 3 =

9 4 5

3 7 8

1 2 3

The resultant matrix after addition:

10 6 8

7 12 14

4 6 5

**Case 2:**

Enter the number of row and column of first matrix = 2 2

Enter the first matrix of order 2 x 2 =

5 1

4 3

Enter the number of row and column of second matrix = 2 3

Enter the second matrix of order 2 x 3 =

9 1 6

4 2 2

Matrices are of different order,hence addition is not possible

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