require 'matrix'
 
size = 3
range = 4
num = 10000
det_is_zero=0
 
matriz = Matrix.build(size) {|i,j| i+j}
print matriz;puts
 
 
for i in 1..num
	a = Array.new
	matriz = Matrix.build(size) { rand -range..range}
	matriz = matriz+matriz.transpose
	#matriz.to_a.each {|r| puts r.inspect}
	det = matriz.determinant
	#puts det
	if det ==0
		det_is_zero+=1
	end
end
puts "Matriz #{size}*#{size} valor de #{-range} a #{range}"
puts "#{num}veces, #{det_is_zero}matrizes não invertiveis,"
puts 1.0*det_is_zero/num
 
 
=begin
for n in 1..10
	for i in 0..3
		Array.new(4) {|i| i.to_s }
		for j in 0..3
 
		end
	end
end
 
 
# Create a 2x2 matrix
m = Matrix[[1, 2], [3, 4]]
 
# Calculate the determinant
det = m.determinant
 
puts m
p m
 
p m[1,0]
puts "The determinant of the matrix is #{det}"
 
=end
 
 
 

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