C Program for Matrix Multiplication: A Beginner’s Guide with Examples & Practice

Matrix multiplication is a cornerstone of programming, used in graphics, data science, and engineering. If you’re learning C, mastering this concept will boost your coding skills. In this guide, we’ll break down matrix multiplication in C using simple language, practical code examples, and real-life applications. Let’s get started!

What is Matrix Multiplication?

Matrix multiplication involves multiplying two matrices to produce a third matrix. Unlike simple arithmetic, it follows specific rules:
Rule 1: The number of columns in the first matrix must equal the rows in the second matrix.
– Rule 2: The resulting matrix has the same rows as the first matrix and the same columns as the second matrix.

Example:
If Matrix A is 2×3 and Matrix B is 3×2, the result will be a 2×2 matrix.

Step-by-Step C Program for Matrix Multiplication
Let’s write a C program to multiply two matrices. We’ll use a x3 matrix for simplicit

#include <stdio.h>

int main() {
    int a[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; // First matrix
    int b[3][3] = {{9, 8, 7}, {6, 5, 4}, {3, 2, 1}}; // Second matrix
    int result[3][3]; // Result matrix
    int i, j, k;

    // Multiply matrices
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            result[i][j] = 0; // Initialize to 0
            for (k = 0; k < 3; k++) {
                result[i][j] += a[i][k] * b[k][j];
            }
        }
    }

    // Print result
    printf("Result:\n");
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            printf("%d ", result[i][j]);
        }
        printf("\n");
    }

    return 0;
}

OutPut

Result:
30 24 18  
84 69 54  
138 114 90  

Explanation:

1. Nested Loops: Three loops are used:
   • i iterates over rows of the first matrix.
   • j iterates over columns of the second matrix.
   • k handles the element-wise multiplication and summation.
2. Result Initialization: Each element of result is set to 0 before calculation to avoid garbage values.

Dynamic Memory Allocation for Flexible Matrix Sizes

For matrices of variable sizes, use dynamic memory allocation with malloc:

#include <stdio.h>
#include <stdlib.h>

int main() {
    int rows1 = 2, cols1 = 3; // Matrix A: 2x3
    int rows2 = 3, cols2 = 2; // Matrix B: 3x2

    // Allocate memory
    int **a = (int **)malloc(rows1 * sizeof(int *));
    int **b = (int **)malloc(rows2 * sizeof(int *));
    int **result = (int **)malloc(rows1 * sizeof(int *));

    // Initialize matrices (code for input omitted for brevity)
    // ... perform multiplication ...

    // Free memory after use
    free(a);
    free(b);
    free(result);

    return 0;
}

Real-Life Applications of Matrix Multiplication

• Computer Graphics: Transform 3D objects (e.g., rotating a character in a game).
• Machine Learning: Training neural networks using weight matrices.
• Physics Simulations: Calculating forces in systems with multiple variables.

Practice Questions

Test your understanding with these exercises:

1. Easy: Modify the static program to multiply a 2×2 matrix.
2. Medium: Add error handling to check if multiplication is possible (columns of A ≠ rows of B).
3. Hard: Optimize the multiplication code to reduce time complexity (research Strassen’s Algorithm).

FAQs

Q1: Why do we initialize the result matrix to 0?

The result matrix must start at 0 to correctly accumulate the sum of products. Otherwise, garbage values will distort the result.

Q2: Can I multiply a 2×3 matrix with a 2×2 matrix?

No! The columns of the first matrix (3) must match the rows of the second matrix (2).

Q3: How to handle very large matrices?

Use dynamic memory allocation (like malloc in C) to avoid stack overflow.

Q4: What’s the time complexity of matrix multiplication?

O(n³) for two n x n matrices due to three nested loops.

Key Takeaways

• Use nested loops for element-wise multiplication.
• Always check if matrices are compatible (columns of A = rows of B).
• Dynamic allocation is essential for flexible matrix sizes.

Try coding these examples yourself, and experiment with the practice questions.