For each of the following payoff matrices, use appropriate methods to find the optimal solution and the value of the game. You may use pure strategies, short-cuts and matrix reduction as needed.

(a) [[2,3],[1,4]]_

((b) )[[1,3],[4,0]]_(

(c) )[[-12,9,-5,0],[4,7,2,1],[0,-5,10,-3]]_(

(d) )[[8,-1,-3,6],[-3,10,8,-4],[3,-4,-5,4]]

For the given matrix below prove or disprove that the given strategy pair is a solution to the game. Hint: computer security levels to have information about v_(1) and v_(2). A=[[-1,1,2,0],[4,-2,-3,2],[0,3,1,-2]]quad{:[X_(1)=(1)/(27)(18","7","2)],[Y_(1)=(1)/(27)(2","12","0","13)]:}