Solve the matrix game. B -3 3-2 01-2 -3 -2 -1

8. (i)Redo: For what type of square matrices A will the algebraic system Ax = 2x have solutions other than x = 0? { Here x is an nx1 real matrix & A is an nxn real matrix.} Hints: 1) Ix = x. 2) Use GP appropriately; 3) Such matrices A must satisfy a certain relation.

5. In each part below, give a m x n matrix R in reduced row-echelon form satisfying the given condition, or explain briefly why it is impossible to do so. (a) m = 3, n = 4, and the equation Rx = c has a solution for all c. (b) m = 3, n = 4, and the equation Rx = 0 has a unique solution. (c) m = 4, n = 3, and the equation Rx = c has a solution for all c. (d) m = 4, n = 3, and the equation Rx = 0 has a unique solution. %3D (e) m = 4, n = 4, and the equation Rx = 0 has no solution. (f) m = 4, n = 4, and the equation Rx O has a nontrivial solution. (g) m = 4, n = 4, and for every c the equations Rx = c have a solution containing a free parameter.

which option is right?

The payoff matrix for a game is   −2 4 6   −2 1 1 1 −1 1 . (a) Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column player C uses the minimax pure strategy.(b) Find the expected payoff to the row player if R uses the maximin strategy 50% of the time and chooses each of the other two rows 25% of the time while C uses the minimax strategy 60% of the time and chooses each of the other two columns 20% of the time. (Round your answer to two decimal places.)

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