Use properties of matrix addition and multiplication to deduce from Problem 25 that if P * and

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Use properties of matrix addition and multiplication to deduce from Problem 25 that if P* and Q* are optimal strategies for the game M with value v, then they are also optimal strategies for the game M + kJ with value v + k.


Data from Problem 25

Let P and Q be strategies for the 2 × 2 matrix game M. Let k be a constant, and let J be the matrix with all 1’s as entries. Show that the matrix product P(kJ) Q equals the 1 × 1 matrix k.

Generalize part (A) to the situation where M and J are m × n matrices.

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Finite Mathematics For Business Economics Life Sciences And Social Sciences

ISBN: 9780134862620

14th Edition

Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker

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