Write C Program to Find the Sum of Each Row and Column of a 2x2 Matrix  -  15 marksSample InputEnter the co-efficients of the matrix

Break Down the Problem

1. We need to create a C program that can read a 2x2 matrix.
2. We will then calculate the sum of each row and each column of the matrix.
3. Finally, we will output the sums.

Relevant Concepts

• A 2x2 matrix can be represented as follows: $\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$
• The sum of each row and each column can be calculated as:
  • Row 1 sum: $S_{row1} = a_{11} + a_{12}$
  • Row 2 sum: $S_{row2} = a_{21} + a_{22}$
  • Column 1 sum: $S_{col1} = a_{11} + a_{21}$
  • Column 2 sum: $S_{col2} = a_{12} + a_{22}$

Analysis and Detail

1. Read the matrix input from the user.
2. Calculate the sums as defined above.
3. Display the sums to the user.

C Program Code

Here's the C program that accomplishes this:

#include <stdio.h>

int main() {
    int matrix[2][2];
    int rowSum[2] = {0, 0};
    int colSum[2] = {0, 0};

    // Input matrix
    printf("Enter the coefficients of the matrix (2x2):\n");
    for(int i = 0; i < 2; ++i) {
        for(int j = 0; j < 2; ++j) {
            printf("Element [%d][%d]: ", i+1, j+1);
            scanf("%d", &matrix[i][j]);
        }
    }

    // Calculate sums
    for(int i = 0; i < 2; ++i) {
        for(int j = 0; j < 2; ++j) {
            rowSum[i] += matrix[i][j];
            colSum[j] += matrix[i][j];
        }
    }

    // Display results
    printf("Sum of rows:\n");
    for(int i = 0; i < 2; ++i) {
        printf("Row %d: %d\n", i+1, rowSum[i]);
    }

    printf("Sum of columns:\n");
    for(int j = 0; j < 2; ++j) {
        printf("Column %d: %d\n", j+1, colSum[j]);
    }

    return 0;
}

Verify and Summarize

• The program initializes a 2x2 matrix and sums up the rows and columns as required.
• Each element is read and stored, followed by calculations based on the defined formulas.

Final Answer

This C program successfully computes the sum of each row and column of a 2x2 matrix as required.