# test_solve.rb  uses ruby  matrix  
require 'matrix'
puts "test_solve.rb running"

# consider these three linear equations in three variables:
# 2x + 10y + 8z = 54 
# 0x +  7y + 4z = 30 
# 5x +  5y + 5z = 35
# To solve these equations, create the two matrices:
 
coefficients = Matrix[[Complex(2.0,0.0), Complex(10,0), Complex(8,0)],
                      [Complex(0.0,0.0), Complex(7,0),  Complex(4,0)],
                      [Complex(5.0,0.0), Complex(5.0),  Complex(5,0)]]
puts "coefficients = Matrix[[Complex(2.0,0.0), Complex(10,0), Complex(8,0)],"
puts "                      [Complex(0.0,0.0), Complex(7,0),  Complex(4,0)],"
puts "                      [Complex(5.0,0.0), Complex(5.0),  Complex(5,0)]]"
puts " "
puts coefficients
puts " "

constants = Matrix[[Complex(54.0)], [Complex(30,0)], [Complex(35,0)]]
puts "constants = Matrix[[Complex(54.0)], [Complex(30,0)], [Complex(35,0)]]"
puts constants
puts " "
# Take the inverse of the coefficient matrix, and multiply it by the results matrix.
# The result will be a matrix containing the values for your variables.
solutions = coefficients.inverse * constants
# => Matrix[[Complex(1,0)], [Complex(2,0)], [Complex(4,0)]]
puts "solutions = coefficients.inverse * constants"
puts solutions
puts " "
puts "test_solve.rb finished"