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Math 181: Test for Chapter 3: More Matrices

This test may be taken with a calculator and any number of hand-written notes. Computers or books and other printed material, be they copies, printouts, or typed, are not allowed.
Place your answer in space provide for each question. Notice: this page changes every time it is loaded, or re-loaded (refreshed). Be careful to read all of each problem. Because these pages are produced on the WEB, for printed versions of these pages there is a chance that a problem, or its possible answers, will be split across two pages.
Use the following matrices to do the problems 1 through 14.
____________________ 1.
____________________ 2.
____________________ 3.
____________________ 4.
____________________ 5.
____________________ 6.

____________________ 7.
____________________ 8.
____________________ 9.
____________________ 10.
____________________ 11.
____________________ 12.
____________________ 13.

____________________ 14.  
____________________ 15. Find the inverse of the following matrix. Be sure to write out your solution in rational number form, i.e., where each element of the matrix is either an integer or a fraction in p/q form, where p and q are integers, reduced to lowest terms.
____________________ 16. Find the inverse of the following matrix. Be sure to write out your solution in rational number form, i.e., where each element of the matrix is either an integer or a fraction in p/q form, where p and q are integers, reduced to lowest terms.
The matrix P given below represents the payoff matrix for a 2-person zero sum game. Player Ms. Sturm has
____________________ 17.
If player Ms. Sturm uses a mixed strategy of choosing actions such that the probability of each action is given by Then what is the expected value of the game?
____________________ 18.
If player Ms. Sturm uses a mixed strategy of choosing actions such that the probability of each action is given by
____________________ 19.
If player Mr. Drang uses a mixed strategy of choosing actions such that the probability of each action is given by
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©Roger M. Palay     Saline, MI 48176     September, 2010