Read the "What in the World?" at the beginning of this chapter. Rank teams A, B, C, D, E, and F if you are given the following information. Team A beats F, and ties \(\mathrm{C}\) and \(\mathrm{D}\); team \(\mathrm{B}\) beats \(\mathrm{A}, \mathrm{C}\), and \(\mathrm{F}\); team \(\mathrm{C}\) beats \(\mathrm{E}\) and \(\mathrm{F}\) but ties \(\mathrm{A}\); team \(\mathrm{D}\) ties \(\mathrm{A}\) and \(\mathrm{F}\); team \(\mathrm{E}\) beats \(\mathrm{A}\) and \(\mathrm{F}\); team \(\mathrm{F}\) beats \(\mathrm{C}\) and ties \(\mathrm{D}\). If two teams tie, enter 0.5 in the zero-one matrix instead of 1.