Sum of Each Row and Column in a Matrix in C: Program to Find Row and Column Sums

📚 In this tutorial, you will learn:

How to calculate the sum of each row in a matrix
How to calculate the sum of each column in a matrix
How to use arrays to store row and column sums
Step-by-step explanation of the program
Practice exercises to test your understanding

Introduction

In this tutorial, we will learn how to write a C program to find the sum of each row and each column in a matrix.

Finding the sum of rows and columns in a matrix is a fundamental operation in many applications, such as:

Data Analysis: Summarizing data by rows and columns
Image Processing: Calculating brightness sums
Statistics: Finding marginal totals in contingency tables
Finance: Calculating row and column totals in spreadsheets

💡 Key Point: Row sum = sum of all elements in a row. Column sum = sum of all elements in a column. We calculate both by traversing the matrix.

Visual Example

Matrix (3×3):

[1  2  3]
[4  5  6]
[7  8  9]

Row Sums:

Row 0: 1 + 2 + 3 = 6
Row 1: 4 + 5 + 6 = 15
Row 2: 7 + 8 + 9 = 24

Column Sums:

Column 0: 1 + 4 + 7 = 12
Column 1: 2 + 5 + 8 = 15
Column 2: 3 + 6 + 9 = 18

C Program to Find Sum of Each Row and Each Column

#include <stdio.h>

int main() {
    int rows, cols, i, j;
    
    // Ask user for matrix dimensions
    printf("Enter the number of rows: ");
    scanf("%d", &rows);
    printf("Enter the number of columns: ");
    scanf("%d", &cols);
    
    // Declare matrix and sum arrays
    int matrix[rows][cols];
    int row_sum[rows];
    int col_sum[cols];
    
    // Initialize sum arrays to 0
    for(i = 0; i < rows; i++) {
        row_sum[i] = 0;
    }
    for(j = 0; j < cols; j++) {
        col_sum[j] = 0;
    }
    
    // Read elements into the matrix
    printf("\nEnter %d elements:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("matrix[%d][%d] = ", i, j);
            scanf("%d", &matrix[i][j]);
        }
    }
    
    // Calculate row and column sums
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            row_sum[i] += matrix[i][j];   // Add to row sum
            col_sum[j] += matrix[i][j];   // Add to column sum
        }
    }
    
    // ====== DISPLAY MATRIX ======
    printf("\n=== The Matrix (%d×%d) ===\n", rows, cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }
    
    // ====== DISPLAY ROW SUMS ======
    printf("\n=== Row Sums ===\n");
    for(i = 0; i < rows; i++) {
        printf("Row %d sum: %d\n", i + 1, row_sum[i]);
    }
    
    // ====== DISPLAY COLUMN SUMS ======
    printf("\n=== Column Sums ===\n");
    for(j = 0; j < cols; j++) {
        printf("Column %d sum: %d\n", j + 1, col_sum[j]);
    }
    
    // ====== DISPLAY MATRIX WITH ROW AND COLUMN SUMS ======
    printf("\n=== Matrix with Row and Column Sums ===\n");
    // Print column headers
    printf("\t");
    for(j = 0; j < cols; j++) {
        printf("C%d\t", j + 1);
    }
    printf("Row Sum\n");
    
    // Print matrix with row sums
    for(i = 0; i < rows; i++) {
        printf("R%d\t", i + 1);
        for(j = 0; j < cols; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("%d\n", row_sum[i]);
    }
    
    // Print column sums at the bottom
    printf("\t");
    for(j = 0; j < cols; j++) {
        printf("%d\t", col_sum[j]);
    }
    printf("Total\n");
    
    // Print grand total
    int grand_total = 0;
    for(i = 0; i < rows; i++) {
        grand_total += row_sum[i];
    }
    printf("\nGrand Total: %d\n", grand_total);
    
    return 0;
}

Sample Output

Enter the number of rows: 3
Enter the number of columns: 3

Enter 9 elements:
matrix[0][0] = 1
matrix[0][1] = 2
matrix[0][2] = 3
matrix[1][0] = 4
matrix[1][1] = 5
matrix[1][2] = 6
matrix[2][0] = 7
matrix[2][1] = 8
matrix[2][2] = 9

=== The Matrix (3×3) ===
1	2	3
4	5	6
7	8	9

=== Row Sums ===
Row 1 sum: 6
Row 2 sum: 15
Row 3 sum: 24

=== Column Sums ===
Column 1 sum: 12
Column 2 sum: 15
Column 3 sum: 18

=== Matrix with Row and Column Sums ===
	C1	C2	C3	Row Sum
R1	1	2	3	6
R2	4	5	6	15
R3	7	8	9	24
	12	15	18	Total

Grand Total: 45

Example with a 2×4 Matrix:

Enter the number of rows: 2
Enter the number of columns: 4

Enter 8 elements:
matrix[0][0] = 1
matrix[0][1] = 2
matrix[0][2] = 3
matrix[0][3] = 4
matrix[1][0] = 5
matrix[1][1] = 6
matrix[1][2] = 7
matrix[1][3] = 8

=== The Matrix (2×4) ===
1	2	3	4
5	6	7	8

=== Row Sums ===
Row 1 sum: 10
Row 2 sum: 26

=== Column Sums ===
Column 1 sum: 6
Column 2 sum: 8
Column 3 sum: 10
Column 4 sum: 12

=== Matrix with Row and Column Sums ===
	C1	C2	C3	C4	Row Sum
R1	1	2	3	4	10
R2	5	6	7	8	26
	6	8	10	12	Total

Grand Total: 36

Program Explanation

Let's break down the code step by step:

Include Header File: #include <stdio.h> includes the standard input/output library.
Declare Variables:
- int rows, cols; — dimensions of the matrix
- int i, j; — loop counters
Declare Arrays:
- int matrix[rows][cols]; — the main matrix
- int row_sum[rows]; — stores sum of each row
- int col_sum[cols]; — stores sum of each column
Initialize Sum Arrays: Sets all elements of row_sum and col_sum to 0.
Read Matrix: Uses nested loops to read elements into the matrix.
Calculate Row and Column Sums:
- row_sum[i] += matrix[i][j] — adds the element to the row sum
- col_sum[j] += matrix[i][j] — adds the element to the column sum
Display Results: Prints the matrix, row sums, column sums, and a combined table with row/column totals.
Calculate Grand Total: Sum of all row sums (or all column sums).
Return: return 0; indicates successful program execution.

📝 Note: The grand total is the sum of all elements in the matrix. It can be calculated by summing all row sums or all column sums.

Algorithm to Find Row and Column Sums

Step-by-step algorithm:

Start
Read the number of rows (r) and columns (c)
Create row_sum array of size r, initialized to 0
Create col_sum array of size c, initialized to 0
Read r × c elements into the matrix
For i = 0 to r-1:
- For j = 0 to c-1:
  - row_sum[i] += matrix[i][j]
  - col_sum[j] += matrix[i][j]
Print the matrix
Print all row sums
Print all column sums
Print the combined table with row and column totals
End

Function-Based Approach

Here's a version using separate functions for better code organization:

#include <stdio.h>

void calculateRowSums(int matrix[][10], int rows, int cols, int row_sum[]) {
    int i, j;
    for(i = 0; i < rows; i++) {
        row_sum[i] = 0;
        for(j = 0; j < cols; j++) {
            row_sum[i] += matrix[i][j];
        }
    }
}

void calculateColSums(int matrix[][10], int rows, int cols, int col_sum[]) {
    int i, j;
    for(j = 0; j < cols; j++) {
        col_sum[j] = 0;
        for(i = 0; i < rows; i++) {
            col_sum[j] += matrix[i][j];
        }
    }
}

void displayMatrix(int matrix[][10], int rows, int cols) {
    int i, j;
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }
}

int main() {
    int rows, cols, i, j;
    
    printf("Enter rows and columns: ");
    scanf("%d %d", &rows, &cols);
    
    int matrix[10][10];
    int row_sum[10], col_sum[10];
    
    printf("\nEnter %d elements:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            scanf("%d", &matrix[i][j]);
        }
    }
    
    calculateRowSums(matrix, rows, cols, row_sum);
    calculateColSums(matrix, rows, cols, col_sum);
    
    printf("\n=== Matrix ===\n");
    displayMatrix(matrix, rows, cols);
    
    printf("\n=== Row Sums ===\n");
    for(i = 0; i < rows; i++) {
        printf("Row %d: %d\n", i + 1, row_sum[i]);
    }
    
    printf("\n=== Column Sums ===\n");
    for(j = 0; j < cols; j++) {
        printf("Column %d: %d\n", j + 1, col_sum[j]);
    }
    
    return 0;
}

Time and Space Complexity

Operation	Time Complexity	Space Complexity
Reading Matrix	O(r × c)	O(1)
Calculating Sums	O(r × c)	O(1)
Overall	O(r × c)	O(r + c)

💻 Practice Exercise

Challenge 1: Find the row with the maximum sum and the column with the maximum sum.

Challenge 2: Calculate the sum of the main diagonal and the sum of the secondary diagonal in addition to row and column sums.

🔍 Click to Show Solution for Challenge 1

#include <stdio.h>

int main() {
    int rows, cols, i, j;
    
    printf("Enter rows and columns: ");
    scanf("%d %d", &rows, &cols);
    
    int matrix[rows][cols];
    int row_sum[rows], col_sum[cols];
    
    for(i = 0; i < rows; i++) {
        row_sum[i] = 0;
    }
    for(j = 0; j < cols; j++) {
        col_sum[j] = 0;
    }
    
    printf("\nEnter %d elements:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            scanf("%d", &matrix[i][j]);
            row_sum[i] += matrix[i][j];
            col_sum[j] += matrix[i][j];
        }
    }
    
    // Find row with maximum sum
    int max_row_sum = row_sum[0];
    int max_row_index = 0;
    for(i = 1; i < rows; i++) {
        if(row_sum[i] > max_row_sum) {
            max_row_sum = row_sum[i];
            max_row_index = i;
        }
    }
    
    // Find column with maximum sum
    int max_col_sum = col_sum[0];
    int max_col_index = 0;
    for(j = 1; j < cols; j++) {
        if(col_sum[j] > max_col_sum) {
            max_col_sum = col_sum[j];
            max_col_index = j;
        }
    }
    
    printf("\n=== Row Sums ===\n");
    for(i = 0; i < rows; i++) {
        printf("Row %d: %d\n", i + 1, row_sum[i]);
    }
    
    printf("\n=== Column Sums ===\n");
    for(j = 0; j < cols; j++) {
        printf("Column %d: %d\n", j + 1, col_sum[j]);
    }
    
    printf("\n✅ Row with maximum sum: Row %d (Sum = %d)\n", 
           max_row_index + 1, max_row_sum);
    printf("✅ Column with maximum sum: Column %d (Sum = %d)\n", 
           max_col_index + 1, max_col_sum);
    
    return 0;
}

Frequently Asked Questions

1. How do you find the sum of each row in a matrix in C?

Use a loop to iterate through each row, and within each row, use an inner loop to add all elements in that row. Store the result in an array.

2. How do you find the sum of each column in a matrix in C?

Use nested loops where the outer loop iterates over columns and the inner loop iterates over rows, adding each element to the column sum.

3. Can you calculate row and column sums in a single loop?

Yes, you can calculate both row and column sums in the same nested loop as shown in the program above.

4. What is the grand total of a matrix?

The grand total is the sum of all elements in the matrix. It can be calculated by summing all row sums or all column sums.

5. What is the time complexity of finding row and column sums?

The time complexity is O(r × c), where r is the number of rows and c is the number of columns.

💡 Tip: Row and column sums are often used in data analysis to find marginal totals. They are also used in image processing to calculate brightness sums.

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