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Two-Dimensional Numeric Array (C)

Learning Objectives

• Declare and initialize 2D numeric arrays.
• Perform addition, subtraction, multiplication, and transpose.
• Compute element addresses in row-major and column-major order.

Concept

A 2D array stores values in rows and columns. In C, memory is stored in row-major order by default.

Algorithm (Matrix Addition)

1. Read matrix dimensions r and c.
2. Input matrix A[r][c] and B[r][c].
3. For each cell (i, j), compute C[i][j] = A[i][j] + B[i][j].
4. Print matrix C.

C Example

#include <stdio.h>

int main(void) {
    int r = 2, c = 3;
    int A[2][3] = {{1, 2, 3}, {4, 5, 6}};
    int B[2][3] = {{6, 5, 4}, {3, 2, 1}};
    int C[2][3];

    for (int i = 0; i < r; i++) {
        for (int j = 0; j < c; j++) {
            C[i][j] = A[i][j] + B[i][j];
        }
    }

    printf("Result (A + B):\n");
    for (int i = 0; i < r; i++) {
        for (int j = 0; j < c; j++) {
            printf("%d ", C[i][j]);
        }
        printf("\n");
    }

    int i = 1, j = 2;
    int cols = 3;
    int base = 1000;      // assumed base address
    int size = sizeof(int);
    int row_major_addr = base + ((i * cols + j) * size);
    printf("Address of A[1][2] (row-major formula): %d\n", row_major_addr);

    return 0;
}

Dry Run (Addition)

• A[0][1] = 2, B[0][1] = 5 -> C[0][1] = 7
• A[1][2] = 6, B[1][2] = 1 -> C[1][2] = 7

Output matrix:

7 7 7
7 7 7

Common Mistakes

• Mismatched matrix dimensions for operations.
• Wrong loop bounds (i < r, j < c).
• Confusing row-major and column-major formulas.

Practice

1. Write matrix subtraction.
2. Write matrix transpose.
3. Implement 2x2 matrix multiplication.