Step by Step solution about How to resolve the algorithm Gauss-Jordan matrix inversion step by step in the Ruby programming language

This Ruby code demonstrates working with matrices using the 'matrix' library. Here's a breakdown of what it does:

1. require 'matrix': This line imports the 'matrix' library, which provides classes and methods for working with matrices in Ruby.

2. m = Matrix[...] creates a 4x4 matrix 'm' with the provided values:

   • The rows of the matrix are enclosed within square brackets [].
   • Each row is separated by commas.
   • The elements within each row are separated by commas.
   • The matrix is assigned to the variable 'm'.

3. m.inv: This expression calculates the inverse of matrix 'm'. The inverse of a matrix is a matrix that, when multiplied by the original matrix, produces the identity matrix (a matrix with 1s on the diagonal and 0s elsewhere).

4. .row_vectors: This method returns a hash of row vectors from the inverted matrix. The keys are integers representing the row indices, and the values are vectors (1x4 matrices) representing the corresponding rows of the inverted matrix.

5. pp m.inv.row_vectors: This line uses the 'pretty print' (pp) method to display the row vectors in a human-readable format. It prints each row vector on a separate line.

In summary, this code creates a matrix, calculates its inverse, and then prints the row vectors of the inverted matrix. It demonstrates how to work with matrices and perform mathematical operations on them using the Ruby 'matrix' library.

require 'matrix'

m = Matrix[[-1, -2, 3, 2],
           [-4, -1, 6, 2],
           [ 7, -8, 9, 1],
           [ 1, -2, 1, 3]]

pp m.inv.row_vectors