R Program to Find the Transpose of a Matrix

Introduction

The transpose of a matrix is obtained by swapping the rows and columns of the matrix. In R, you can easily compute the transpose of a matrix using built-in functions. This guide will walk you through writing an R program that finds the transpose of a matrix.

Problem Statement

Create an R program that:

• Creates a matrix.
• Finds the transpose of the matrix.
• Displays the original and the transposed matrix.

Example:

• Input:
  • Matrix A (2×3): 1 2 3 | 4 5 6
• Output:
  • Transposed Matrix (3×2): 1 4 | 2 5 | 3 6

Solution Steps

1. Create a Matrix: Use the matrix() function to create a matrix.
2. Find the Transpose of the Matrix: Use the t() function to transpose the matrix.
3. Display the Original and Transposed Matrices: Use the print() function to display both the original and transposed matrices.

R Program

# R Program to Find the Transpose of a Matrix
# Author: Ramesh Fadatare

# Step 1: Create a matrix
matrix_A <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3)

# Step 2: Find the transpose of the matrix
transpose_matrix <- t(matrix_A)

# Step 3: Display the original and transposed matrices
print("Original Matrix A:")
print(matrix_A)

print("Transposed Matrix:")
print(transpose_matrix)

Explanation

Step 1: Create a Matrix

• The matrix() function is used to create matrix_A, a 2×3 matrix with elements 1, 2, 3, 4, 5, 6.

Step 2: Find the Transpose of the Matrix

• The t() function is used to transpose the matrix. The transpose operation swaps the rows and columns of the matrix, resulting in a 3×2 matrix.

Step 3: Display the Original and Transposed Matrices

• The print() function is used to display both the original matrix and the transposed matrix, allowing you to see the transformation.

Output Example

Example:

[1] "Original Matrix A:"
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

[1] "Transposed Matrix:"
     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    5    6

Conclusion

This R program demonstrates how to find the transpose of a matrix using the t() function. It covers basic matrix operations such as matrix creation, transposition, and displaying the results. Understanding how to transpose a matrix is essential in various mathematical and data analysis applications, making this example valuable for anyone learning R programming.