SOLVED:Show that the elimination method of computing the value of the determinant of an n ×n matrix involves [n(n-1)(2 n-1)] / 6 additions and [(n1)(n^2 n 3)] / 3 multiplications and divisions. Hint: At the ith step of the reduction process, it takes n-i divisions to calculate the multiples of the ith row that are to be subtracted from the remaining rows below the pivot. We must then calculate new values for the (n-i)^2 entries in rows i 1 through n and columns i 1 through n.
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This method is just like the plurality-with-elimination method except that in each round we eliminate the candidate with the largest number of lastplace votes (instead of the one with the fewest first-place votes). (a) Find the winner of the Math Club election using the Coombs method. (b) Give an example that illustrates why the Coombs method violates the Condorcet criterion. (c) Give an example that illustrates why the Coombs method violates the monotonicity criterion. | Numerade
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Top-two IRV is a variation of the plurality-with-elimination method in which all the candidates except the top two are eliminated in the first round (see Exercises 39 and 40 ). (a) Use the Math Club election to show that top-two IRV can produce a different outcome than plurality-withelimination. (b) Give an example that illustrates why top-two IRV violates the monotonicity criterion. (c) Give an example that illustrates why top-two IRV violates the Condorcet criterion. | Numerade
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