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    Python3:

    if __name__ == "__main__":
      # Compute the 3 x 3 determinant of the system
      # Determinant = 0, when system of equations has *NO SOLUTIONS*
      det = lambda a: a*(2*a - 1) - 1*(a - 2) + 2*(1 - 4)
      
      # Hold all possible alpha values
      lst = list()
      
      # Loop through several values that make det = 0
      for i in range(-100, 101):
        if det(i) == 0:
          lst += [i]
          
      # Return the minimum value
      print(min(lst))