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Explanation of Matrix Multiplication in C

Matrix multiplication is a fundamental operation in linear algebra and is often used in various computational tasks. In C, matrix multiplication can be performed using nested loops to iterate over the elements of the matrices and calculate the resulting matrix.

Here is an example of how matrix multiplication can be implemented in C:

#include <stdio.h>

#define ROW_A 2
#define COL_A 3
#define ROW_B 3
#define COL_B 2

void matrixMultiplication(int A[ROW_A][COL_A], int B[ROW_B][COL_B], int C[ROW_A][COL_B]) {
    int i, j, k;

    for (i = 0; i < ROW_A; i++) {
        for (j = 0; j < COL_B; j++) {
            C[i][j] = 0;
            for (k = 0; k < COL_A; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
}

int main() {
    int A[ROW_A][COL_A] = {{1, 2, 3}, {4, 5, 6}};
    int B[ROW_B][COL_B] = {{7, 8}, {9, 10}, {11, 12}};
    int C[ROW_A][COL_B];

    matrixMultiplication(A, B, C);

    printf("Resultant matrix C:\n");
    for (int i = 0; i < ROW_A; i++) {
        for (int j = 0; j < COL_B; j++) {
            printf("%d ", C[i][j]);
        }
        printf("\n");
    }

    return 0;
}

In this example, we have two matrices, A and B, with dimensions (2x3) and (3x2) respectively. The resulting matrix C will have dimensions (2x2). The matrixMultiplication function takes the input matrices A and B, and calculates the resulting matrix C using nested loops. The outer loops iterate over the rows of A and the columns of B, while the inner loop performs the dot product of the corresponding row of A and column of B.

The resulting matrix C is then printed using the printf function.

Note: This is just one way to implement matrix multiplication in C. There are other approaches and optimizations that can be applied depending on the specific requirements and constraints of the problem.

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