#
# Linear Equation (without pivoting)
#
def gj(x)
  row=x.size 
  col=row+1
  a=Array.new(x.size){|i| x[i].dup}
  for k in 0..(row-1)
    # normalize a[k][i] s.t. a[k][k]=1
    akk = a[k][k]
    for i in 0..(col-1)
      a[k][i]=a[k][i]/akk
    end
    # adjust i-th row s.t. a[i][k]=0,  skipping k-th row
    for i in 0..(row-1)
      if i != k
        aik = a[i][k]
        for j in k..(col-1)
          a[i][j] = a[i][j] - aik * a[k][j]
        end
      end
    end
  end
  Array.new(row){|i| a[i][row]}
end

# a = [[1.0,1.0,-1.0,2.0],
#        [3.0,5.0,-7.0,0.0],
#        [2.0,-3.0,1.0,5.0]]
# a = [[1.0,  -50.0, -3.0,  -90.0],
#      [-85.0,  2.0,  -25.0, -6.0],
#     [79.0,  5.0,  30.0, -1.0]]
# p gj(a)