Step by Step solution about How to resolve the algorithm Matrix transposition step by step in the Ruby programming language

The provided Ruby code deals with transposing matrices, a mathematical operation that flips a matrix over its diagonal. There are two distinct methods for accomplishing this transposition: using the transpose method of the Matrix class and implementing a custom transpose function.

1. Transposing with Matrix class:

Here, the transpose method built into the Matrix class is used to transpose the matrix m. The Matrix class provides a convenient way to represent and manipulate matrices in Ruby. The transpose method swaps the rows and columns of the matrix, effectively flipping it over its diagonal.

Example:

require 'matrix'

m = Matrix[[1, 1, 1, 1],
         [2, 4, 8, 16],
         [3, 9, 27, 81],
         [4, 16, 64, 256],
         [5, 25, 125, 625]]

puts m.transpose

2. Custom transpose function:

This code defines a custom transpose function that manually performs the transposition of a matrix. It takes a matrix m as input and returns the transposed matrix. The function uses Ruby's zip method to combine the elements of each column into rows, resulting in the transposed matrix.

Example:

def transpose(m)
 m[0].zip(*m[1..-1])
end

p transpose([[1, 2, 3], [4, 5, 6]])

In summary, both approaches achieve the same result of transposing a matrix. The Matrix class provides a built-in transpose method for convenience, while the custom transpose function demonstrates a manual implementation of the transposition operation.

m=[[1,  1,  1,   1],
   [2,  4,  8,  16],
   [3,  9, 27,  81],
   [4, 16, 64, 256],
   [5, 25,125, 625]]
puts m.transpose

require 'matrix'

m=Matrix[[1,  1,  1,   1],
         [2,  4,  8,  16],
         [3,  9, 27,  81],
         [4, 16, 64, 256],
         [5, 25,125, 625]]
puts m.transpose

def transpose(m)
  m[0].zip(*m[1..-1])
end
p transpose([[1,2,3],[4,5,6]])