2. Which of the following facts about a one period market with S = 4 states, N = 5 securities, and payoff matrix D individually constitutes a sufficient condition for the existence of a risk- free payoff (i.e. a payoff 1 R$)? Explain why or why not for each. (a) Rank(D) = Rank(D'). (Here D' denoted the transpose of the matrix D.) (b) Rank(D) = 4. (c) The market does not permit arbitrage. (d) The market is complete. (e) $1 invested in security 1 at time 0 pays off $ 2 at time T in any state. (f) A unique state price vector exists.