In Exercises 310, find an LU-decomposition of the coefficient matrix, and then use the method of Example 1 to solve the system.
Koshar Amy Brogan March 28,30 & April 1, 2016 Apportionment Part 3 Review: Spread 10 calculators among 4 classes by population using the following methods. Class A: 87 Class B: 45 Class C: 96 Class D: 62 Hamilton Method Class A Class B Class C Class D Jefferson Method Class A Class B Class C Class D Webster Method Class A Class B Class C Class D Write out the results in full sentences. (Answers at the end of the Notes) Hill-Huntington Method Arithmetic Mean o The product of two numbers that have been added together; the average o (a*b)/2 Geometric Mean o The square root of the product of two numbers o √ ∗ In the Hill-Huntington Method, the quotas are rounded by the Geometric Mean instead of the usual way. When the quota is a decimal, for example 3.14, then we would take the square root of 3*4 to see if the amount would round up or down. The Geometric Mean is usually close to the .5 value, but the smaller the numbers the further the distance from the midpoint, such as in the table below. Numbers Usual round limit Geometric Mean Equation Geometric Cut-Off (Approximate) 1-2 1.5 √1 ∗ 2 1.41 2-3 2.5 √2 ∗ 3
