Example: Matrix Multiplication using Arrays in C

// Matrix Multiplication using Arrays
#include <stdio.h>

#define MAX_SIZE 10 // Define a maximum size for demonstration purposes

int main() {
    int r1, c1, r2, c2; // Variables for rows and columns of matrix1, matrix2

    // Step 1: Get dimensions for the first matrix from the user
    printf("Enter number of rows for first matrix: ");
    scanf("%d", &r1);
    printf("Enter number of columns for first matrix: ");
    scanf("%d", &c1);

    // Step 2: Get dimensions for the second matrix from the user
    printf("Enter number of rows for second matrix: ");
    scanf("%d", &r2);
    printf("Enter number of columns for second matrix: ");
    scanf("%d", &c2);

    // Step 3: Check for compatibility before multiplication
    // The number of columns in the first matrix must equal the number of rows in the second matrix.
    if (c1 != r2) {
        printf("\nError: Number of columns of the first matrix must be equal to the number of rows of the second matrix.\n");
        printf("Matrix multiplication is not possible with these dimensions.\n");
        return 1; // Indicate an error
    }

    // Declare 2D arrays for matrices and the result
    int matrix1[MAX_SIZE][MAX_SIZE];
    int matrix2[MAX_SIZE][MAX_SIZE];
    int result[MAX_SIZE][MAX_SIZE];

    // Step 4: Get elements for the first matrix from the user
    printf("\nEnter elements of the first matrix:\n");
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c1; j++) {
            printf("Enter element matrix1[%d][%d]: ", i, j);
            scanf("%d", &matrix1[i][j]);
        }
    }

    // Step 5: Get elements for the second matrix from the user
    printf("\nEnter elements of the second matrix:\n");
    for (int i = 0; i < r2; i++) {
        for (int j = 0; j < c2; j++) {
            printf("Enter element matrix2[%d][%d]: ", i, j);
            scanf("%d", &matrix2[i][j]);
        }
    }

    // Step 6: Initialize all elements of the result matrix to zero
    // This is crucial because we will be accumulating sums into these elements.
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c2; j++) {
            result[i][j] = 0;
        }
    }

    // Step 7: Perform matrix multiplication
    // The core logic involves three nested loops:
    // Outer loop (i): Iterates through rows of the first matrix (and result matrix).
    // Middle loop (j): Iterates through columns of the second matrix (and result matrix).
    // Inner loop (k): Iterates through columns of the first matrix (which must match rows of the second matrix).
    // This loop calculates each element result[i][j] by summing products.
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c2; j++) {
            for (int k = 0; k < c1; k++) { // Or k < r2, since c1 == r2
                result[i][j] += matrix1[i][k] * matrix2[k][j];
            }
        }
    }

    // Step 8: Display the resultant matrix
    printf("\nResultant Matrix:\n");
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c2; j++) {
            printf("%d\t", result[i][j]); // Print element followed by a tab
        }
        printf("\n"); // Move to the next line after printing a row
    }

    return 0; // Indicate successful execution
}