Significance of arrays; multiply 3×3 matrices

Significance of arrays

• An array stores many values of the same type under one name, so a hundred variables are not needed.
• Elements are reached quickly by index (a[i]), which works well with loops.
• Data are stored in consecutive memory, so traversal and processing are simple and fast.
• Needed for lists, tables and matrices, and as the base for strings, sorting, searching and many data structures.
• Arrays are passed to functions easily, so one function can work on a whole set of data.

Program: multiply two 3×3 matrices

c[i][j] = Σ a[i][k] × b[k][j] for k = 0 to 2. The matrices are read in main(), passed to multiply() and the product is displayed in main().

#include <stdio.h>

void multiply(int a[3][3], int b[3][3], int c[3][3])
{
    for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++) {
            c[i][j] = 0;
            for (int k = 0; k < 3; k++)
                c[i][j] += a[i][k] * b[k][j];
        }
}

int main(void)
{
    int a[3][3], b[3][3], c[3][3];
    printf("Enter first matrix: ");
    for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
            scanf("%d", &a[i][j]);
    printf("Enter second matrix: ");
    for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
            scanf("%d", &b[i][j]);

    multiply(a, b, c);
    printf("Product:\n");
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++)
            printf("%5d", c[i][j]);
        printf("\n");
    }
    return 0;
}

Sample run (second matrix is diag(1,1,2))

Input: 1 2 3 4 5 6 7 8 9 1 0 0 0 1 0 0 0 2

Enter first matrix: Enter second matrix: Product:
    1    2    6
    4    5   12
    7    8   18

The third column is doubled, which matches the multiplier matrix.