MOD5_280-282 - 72106 MOD05 GGS 3/30/05 2:48 PM Page 280 M O...

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280 T EACHING S UGGESTIONS Teaching Suggestion M5.1: Why Discuss Matrices and Determinants? These mathematical tools are needed in Markov analysis to com- pute absorbing states. In a more advanced treatment of linear pro- gramming, matrix manipulation skills are also desired. Teaching Suggestion M5.2: Matrices Can Be Used to Display Data in Tabular Form. As seen in Section M5-3 in this module, a matrix is also a useful tool for presenting data. S OLUTIONS TO P ROBLEMS M5-1. Matrices are used in Markov analysis and game theory. They may also be used to represent a system of equations in linear programming. M5-2. One way to calculate the determinant of a matrix is to draw the primary and secondary diagonals. The numbers in each diagonal are multiplied. Each of the products found on a pri- mary diagonal are added, and each of the products found on a secondary diagonal are subtracted. The resulting number is the determinant. M5-3. Determinants are used in solving a system of equations and in Fnding the inverse of a matrix. M5-4. A matrix of cofactors is developed as follows: 1. Select an element in the original matrix. 2. Draw a line through the row and column of the element selected. The numbers uncovered represent the cofactor for that element.
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MOD5_280-282 - 72106 MOD05 GGS 3/30/05 2:48 PM Page 280 M O...

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