Game theory--Two-person; Constant-sum games

The attached file has a problem that I can't figure out how to set up. Can you take a look and explain how this problem should be set up?

optimal strategy for a 2-person zero-sum game using mixed strategies

I have determined the value of the game, but I don't know how to get to the optimal strategy. Please step through. My professor gave us the answer: Row Player Value = 4/3, The optimal strategy for the row player is (2/3,1/3). The optimal strategy for the column player is (2/3, 1/3, 0).

two-person zero-sum game theory 2x3 matrix

My problem is attached. I know how to work problems if the matrix is 2x2, but other sizes of matrices confuse me. Can you help?

Game Theory and solving using LP

Attached is a 2-person zero sum game problem. I have worked it to the point of needing to solve using Linear Programming. I know there are programs that will solve it for me, but I would like to know how to solve it by hand. Would you show me?

Markov Chain

Please see attached. I don't think I have it set up correctly. Can you show me how to set the problem up? I think I know how to solve it if I had it set up correctly.