{"id":1033,"date":"2024-10-21T15:00:09","date_gmt":"2024-10-21T09:30:09","guid":{"rendered":"https:\/\/codexplained.in\/?p=1033"},"modified":"2025-11-24T15:29:56","modified_gmt":"2025-11-24T09:59:56","slug":"matrix-multiplication","status":"publish","type":"post","link":"https:\/\/codexplained.in\/?p=1033","title":{"rendered":"Matrix Multiplication"},"content":{"rendered":"\n

Introduction<\/h3>\n\n\n\n

Matrix multiplication is a fundamental operation in linear algebra where two matrices are multiplied to produce a third matrix. This operation is crucial in various applications, including computer graphics, machine learning, and scientific computations. Unlike addition and subtraction, matrix multiplication involves a more complex calculation of dot products.<\/p>\n\n\n

\n#include <stdio.h>\n\n#define MAX_SIZE 10 \/\/ Define maximum size for the matrices\n\nvoid multiplyMatrices(int a[MAX_SIZE][MAX_SIZE], int b[MAX_SIZE][MAX_SIZE], int result[MAX_SIZE][MAX_SIZE], int rowsA, int colsA, int colsB) {\n    for (int i = 0; i < rowsA; i++) {\n        for (int j = 0; j < colsB; j++) {\n            result[i][j] = 0; \/\/ Initialize the result element\n            for (int k = 0; k < colsA; k++) {\n                result[i][j] += a[i][k] * b[k][j]; \/\/ Calculate the dot product\n            }\n        }\n    }\n}\n\nint main() {\n    int a[MAX_SIZE][MAX_SIZE], b[MAX_SIZE][MAX_SIZE], result[MAX_SIZE][MAX_SIZE];\n    int rowsA, colsA, rowsB, colsB;\n\n    printf("Enter the number of rows and columns for the first matrix: ");\n    scanf("%d %d", &rowsA, &colsA);\n\n    printf("Enter elements of the first matrix:\\n");\n    for (int i = 0; i < rowsA; i++) {\n        for (int j = 0; j < colsA; j++) {\n            printf("a[%d][%d]: ", i, j);\n            scanf("%d", &a[i][j]);\n        }\n    }\n\n    printf("Enter the number of rows and columns for the second matrix (rows must equal cols of first): ");\n    scanf("%d %d", &rowsB, &colsB);\n\n    if (colsA != rowsB) {\n        printf("Matrix multiplication not possible: columns of the first matrix must equal rows of the second.\\n");\n        return 1; \/\/ Exit if matrices cannot be multiplied\n    }\n\n    printf("Enter elements of the second matrix:\\n");\n    for (int i = 0; i < rowsB; i++) {\n        for (int j = 0; j < colsB; j++) {\n            printf("b[%d][%d]: ", i, j);\n            scanf("%d", &b[i][j]);\n        }\n    }\n\n    multiplyMatrices(a, b, result, rowsA, colsA, colsB);\n\n    printf("Resultant matrix after multiplication:\\n");\n    for (int i = 0; i < rowsA; i++) {\n        for (int j = 0; j < colsB; j++) {\n            printf("%d ", result[i][j]);\n        }\n        printf("\\n");\n    }\n\n    return 0;\n}\n<\/pre><\/div>\n\n\n
Explanation<\/h3>\n\n\n\n
    \n
  1. Function Definition<\/strong>:\n
      \n
    • multiplyMatrices(int a[MAX_SIZE][MAX_SIZE], int b[MAX_SIZE][MAX_SIZE], int result[MAX_SIZE][MAX_SIZE], int rowsA, int colsA, int colsB)<\/code>: This function takes two input matrices (a<\/code> and b<\/code>), an empty matrix (result<\/code>) to store the product, and the dimensions of the matrices.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Initialization<\/strong>:\n
        \n
      • The outer loops iterate through each row of matrix a<\/code> and each column of matrix b<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Dot Product Calculation<\/strong>:\n
          \n
        • For each element in the resultant matrix, a third loop calculates the dot product of the respective row of matrix a<\/code> and column of matrix b<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Main Function<\/strong>:\n
            \n
          • Prompts the user for the dimensions and elements of the matrices.<\/li>\n\n\n\n
          • Checks if multiplication is possible (columns of the first matrix must equal rows of the second).<\/li>\n\n\n\n
          • Calls multiplyMatrices<\/code> to perform the multiplication and prints the result.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
            Input<\/h3>\n\n\n\n
            When you run the program, it will prompt for the dimensions and elements of both matrices. For example:<\/p>\n\n\n
            \nEnter the number of rows and columns for the first matrix: 2 3\nEnter elements of the first matrix:\na[0][0]: 1\na[0][1]: 2\na[0][2]: 3\na[1][0]: 4\na[1][1]: 5\na[1][2]: 6\nEnter the number of rows and columns for the second matrix (rows must equal cols of first): 3 2\nEnter elements of the second matrix:\nb[0][0]: 7\nb[0][1]: 8\nb[1][0]: 9\nb[1][1]: 10\nb[2][0]: 11\nb[2][1]: 12\n<\/pre><\/div>\n\n\n
            Output<\/h3>\n\n\n\n
            The output will display the resultant matrix after multiplication:<\/p>\n\n\n
            \nResultant matrix after multiplication:\n58 64 \n139 154\n<\/pre><\/div>\n\n\n
            Conclusion<\/h3>\n\n\n\n
            Matrix multiplication is a crucial operation in various fields of science and engineering. The provided C implementation demonstrates how to multiply two matrices, ensuring that the conditions for multiplication are met. This example highlights the complexity of matrix operations and provides a foundation for further studies in linear algebra and numerical methods.<\/p>\n