Hello there! Are you ready to hone your Ruby programming skills with another exciting exercise? In this unit, we are delving into the world of matrices. More specifically, we'll be transposing a given matrix. Let's dive into this matrix manipulation game without delay!

To begin, let's elaborate on the task at hand. You are required to write a Ruby method named transform_matrix. This method will accept a 2D array (which represents a matrix) that contains integers as inputs. Your responsibility is to return another 2D array, which is the transposed version of the given matrix.

Remember, when we mention 'transposing a matrix,' we are referring to the process of switching its rows and columns. In other words, all the rows of the original matrix should convert into columns in the transposed matrix, and vice versa.

For instance, if the original matrix (input 2D array) is:

Ruby
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1[
2  [1, 2, 3],
3  [4, 5, 6]
4]

Then the transposed matrix (output 2D array) will be:

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1[
2  [1, 4],
3  [2, 5],
4  [3, 6]
5]

It is vital for your result to maintain the integrity of the data type that is present in the original matrix. In layman's terms, the values seen in the input matrix are integers, and they should be integers in the output matrix as well.

The initial step in building our solution involves determining the dimensions of the matrix. We need to know the number of rows and columns present in it. The Ruby length method can offer this information. The number of rows is simply the length of the matrix (the outer array), and the number of columns matches the length of any of the inner arrays.

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1def transform_matrix(matrix)
2  rows = matrix.length
3  cols = rows > 0 ? matrix[0].length : 0
4end

The subsequent step is to create a "placeholder" for the transposed matrix that is in alignment with its required dimensions. This will be a new 2D array, but with the number of rows and columns swapped. Initially, we can populate this matrix with all zeros.

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1def transform_matrix(matrix)
2  rows = matrix.length
3  cols = rows > 0 ? matrix[0].length : 0
4  result = Array.new(cols) { Array.new(rows, 0) }
5end

It's time to get to the crux of the matter — transposing the matrix. For every element in the original matrix, we want to move it from the ith row and jth column to the jth row and ith column of the transposed matrix. A straightforward nested iteration using times can effortlessly execute this swap for all elements of the matrix.

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1def transform_matrix(matrix)
2  rows = matrix.length
3  cols = rows > 0 ? matrix[0].length : 0
4  result = Array.new(cols) { Array.new(rows, 0) }
5
6  rows.times do |i|
7    cols.times do |j|
8      result[j][i] = matrix[i][j]
9    end
10  end
11
12  result
13end
14
15# Initial matrix (2D array)
16matrix = [
17  [1, 2, 3],
18  [4, 5, 6]
19]
20
21# Call our method on the matrix and output the result
22transposed = transform_matrix(matrix)
23puts transposed.inspect  # Outputs: [[1, 4], [2, 5], [3, 6]]

This step concludes our solution!

Another solution could be written using Ruby's block syntax for direct array creation:

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1def transform_matrix(matrix)
2  rows = matrix.length
3  cols = rows > 0 ? matrix[0].length : 0
4  result = Array.new(cols) { |i| Array.new(rows) { |j| matrix[j][i] } }
5
6  result
7end

Here we fill the matrix directly at creation, and the j-th column of the i-th row of the new matrix is assigned the value matrix[j][i].

• The outer Array.new(cols) creates cols rows for the transposed matrix.
• The block { |i| Array.new(rows) { |j| matrix[j][i] } } populates each column by mapping elements from the original matrix to their new positions. It maps each element from the original matrix's j-th row and i-th column to the i-th row and j-th column of the transposed matrix.

With this, we've brought this lesson to a close! Congratulations on successfully implementing a method that can transpose matrices! This task is not simple, but by accomplishing it, you've exhibited your understanding of and proficiency in Ruby's arrays, loops, and the concept of matrix transposition.

Your hard work continues, though. Now that you have acquired this valuable skill, it's time to reinforce it with more practice. During the next session, you will encounter practice problems that build on this concept. So, get ready and start coding!