linear_algebra.rb

require 'pry'

# A linear algebra matrix row.
class Row
  def initialize(arr)
    @arr = arr.map(&:to_r)
  end

  def map_with_index
    arr = @arr.map.with_index do |val, i|
      yield(val, i)
    end
    Row.new(arr)
  end

  def +(other)
    map_with_index do |val, i|
      val + other[i]
    end
  end

  def -(other)
    map_with_index do |val, i|
      val - other[i]
    end
  end

  def *(other)
    Row.new(@arr.map { |val| (val * other).to_r })
  end

  def [](i)
    @arr[i]
  end

  def to_s
    arr = @arr.map do |val|
      if val.denominator == 1
        val.to_i
      else
        val
      end
    end
    "[ #{arr.join(' ')} ]"
  end
end

matrix = [
  Row.new([-Rational(5, 6), Rational(1, 3), Rational(11, 6), 1, 0, 0]),
  Row.new([0, Rational(2, 3), 2, 0, 1, 0]),
  Row.new([1, -Rational(1, 2), -Rational(5, 2), 0, 0, 1])
]

matrix[0] = matrix[0] * -Rational(6, 5)

matrix[1] = matrix[1] * Rational(3, 2)

matrix[2] = matrix[2] - matrix[0]

matrix[2] = matrix[2] * -10

matrix[2] = matrix[2] - matrix[1]

# matrix[0] = matrix[0] - (matrix[1] * Rational(3, 2))

puts matrix