In a square matrix, the diagonal elements are those that extend from the top left corner to the bottom right corner. For example, in a n\u00d7nn \\times nn\u00d7n matrix, the diagonal elements are located at positions (0,0),(1,1),(2,2),\u2026,(n\u22121,n\u22121)(0,0), (1,1), (2,2), \\ldots, (n-1,n-1)(0,0),(1,1),(2,2),\u2026,(n\u22121,n\u22121). The sum of these diagonal elements can be useful in various mathematical applications, including linear algebra and computer graphics.<\/p>\n\n\n
\n#include <stdio.h>\n\n#define MAX 10 \/\/ Maximum size of the matrix\n\nvoid inputMatrix(int matrix[MAX][MAX], int size) {\n printf("Enter elements of the matrix (%d x %d):\\n", size, size);\n for (int i = 0; i < size; i++) {\n for (int j = 0; j < size; j++) {\n scanf("%d", &matrix[i][j]);\n }\n }\n}\n\nint sumDiagonal(int matrix[MAX][MAX], int size) {\n int sum = 0;\n for (int i = 0; i < size; i++) {\n sum += matrix[i][i]; \/\/ Add diagonal elements\n }\n return sum;\n}\n\nvoid printMatrix(int matrix[MAX][MAX], int size) {\n printf("Matrix (%d x %d):\\n", size, size);\n for (int i = 0; i < size; i++) {\n for (int j = 0; j < size; j++) {\n printf("%d ", matrix[i][j]);\n }\n printf("\\n");\n }\n}\n\nint main() {\n int matrix[MAX][MAX];\n int size;\n\n printf("Enter the size of the matrix: ");\n scanf("%d", &size);\n\n inputMatrix(matrix, size);\n \n printf("Original Matrix:\\n");\n printMatrix(matrix, size);\n \n int diagonalSum = sumDiagonal(matrix, size);\n printf("Sum of diagonal elements: %d\\n", diagonalSum);\n\n return 0;\n}\n<\/pre><\/div>\n\n\nExplanation<\/h3>\n\n\n\n\n- Includes and Defines<\/strong>: The program includes the
stdio.h<\/code> header for input\/output functions and defines a constant MAX<\/code> for the maximum size of the matrix.<\/li>\n\n\n\n- Input Function<\/strong>: The
inputMatrix<\/code> function prompts the user to enter the elements of a square matrix of size size\u00d7sizesize \\times sizesize\u00d7size.<\/li>\n\n\n\n- Sum Function<\/strong>: The
sumDiagonal<\/code> function calculates the sum of the diagonal elements by iterating through the matrix and adding the elements located at positions (i,i)(i, i)(i,i).<\/li>\n\n\n\n- Print Function<\/strong>: The
printMatrix<\/code> function displays the matrix in a formatted manner.<\/li>\n\n\n\n- Main Function<\/strong>: In
main<\/code>, the program:\n\n- Declares a matrix.<\/li>\n\n\n\n
- Asks for the size of the matrix.<\/li>\n\n\n\n
- Calls the input, print, and sum functions to display the results.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
Input<\/h3>\n\n\n\n
The user is prompted to enter the size of the matrix, followed by the matrix elements. Example input:<\/p>\n\n\n
\nEnter the size of the matrix: 3\nEnter elements of the matrix (3 x 3):\n1 2 3\n4 5 6\n7 8 9\n<\/pre><\/div>\n\n\nOutput<\/h3>\n\n\n\n
The program will output the original matrix and the sum of its diagonal elements. For the example input, the output will be:<\/p>\n\n\n
\nOriginal Matrix:\n1 2 3 \n4 5 6 \n7 8 9 \n\nSum of diagonal elements: 15\n<\/pre><\/div>\n\n\nConclusion<\/h3>\n\n\n\n
This C program effectively demonstrates how to find the sum of the diagonal elements in a square matrix. This operation is fundamental in various mathematical contexts and serves as a useful exercise for understanding matrix manipulation in C. The code can be easily modified to handle different matrix sizes or data types, making it adaptable for various applications.<\/p>\n