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Let W be a two-dimensional subspace of n 3. If Tw: n 3 - n

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 42 Chapter 5.4

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 42

Let W be a two-dimensional subspace of n 3. If Tw: n 3 - n 3 is the reflection ofn3 about W.then each nonzero vector

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4/18/16 voter turnout continued changes over recent decades  “puzzle of participation” (1960-1996) o more and more people were achieving higher levels of education o voter registration was becoming easier  shouldn’t voter turnout increase as well  Think of the time o Vietnam war, Watergate scandal etc  mistrust in government  decreased voter turnout  Social capital deteriorating during this time  Declines in political connectedness  Declines in social connectedness (Putnam)  Declines in political mobilization o More voting ineligibles as % of voting age population] Average voter turnout in elections to the lower house 1945-2005 AUSTRALIA (23 ELECTIONS) 95% VOTER TURNOUT ITALY (15) 90% GERMANY (15) 85% ISREAL (16) 80% BRAZIL (14) 78% GREAT BRITAIN (16) 75% FRANCE (16) 75% CANADA (18) 74% SPAIN (8) 74% JAPAN (22) 69% UNITED STATES (14- presidential 55% election years only)  Proportional representation o Winner-take-all plurality in the US o If you win second place in the presidential election, nothing happens o In other countries, these people may receive parliamentary positions or some other form of recognition  Why are we relatively lower to other nations o Legal environment  US is the only nation in the world that forces individuals to self-register o Differences in political [arty environment  Most other nations have up to 8 active parties that can elect members to the legislature. The US has only 2, has only had 2 ever at one time, and will likely only ever have 2  When you have more parties, you have a lot of parties that are tied to lower class and working class and that makes them more likely to vote  In other countries there is little-no relation between likelihood to vote and level of income or education o More elections  On weekdays—prevents working class  Most other nations, elections are “holiday” or they give a 3 day span over the weekend  Voter fatigue What can (should) we do to increase turnout  Civic education  Easier registration  Election day as holiday or weekend  Vote by mail E-mail  Fewer elections  PR system  more parties  Compulaosy voting  IS IT IMPORTANT TO INCREASE VOTER TURNOUT 4/20/16 Political Parties  Why parties  Are parties in decline  Why 2-party system Why  No one wanted to party  Those who founded the country advised AGAINST parties yet created them  2 arguments for what parties are in our government o 1. Democratic theory-based  individual citizens are “deficient” but perhaps intermediary insitutions (parties and interest groups) can bridge the gap between citizens and the government  pluralist theory of democracy  o 2. Functional  parties fulfill numerous functions in a representative democracy  recruit leaders  helo conduct campaigns  nominate candidates for office  list of general election candidates  voting cues  channels for participation  propose policy programs  overcome fragmentation and organize government  watchdog functions  aggregate interests to win elections how to define a party  are parties in decline  3 part conceptualization o 1. Party in electorate  those who go out and vote o 2. Party as organization  those who serve o 3. Party in government  those in office as committees  parties have been resurgent across the past couple of decades (not in decline)  role of party ID in structuring vote choice is stronger than ever o most people identify with a party o even independents lean to 1 side  as organizations, parties are extremely strong right now o national party committees raise hige amounts of money, have large staffs, nice offices, constantly working etc.  intra-party unity in congress quite high o disappearance of conservative coalition why a 2 party system  Historically major US parties are the federalists, wigs, republicans and democrats  only ever 2 at a time  Duvergers law: winner-take-all plurality elections o The way we conduct elections  2 parties o Proportional allocation  more parties o Third parties have basically no chance of electing anyone to office due to our plurality method  1992 election Clinton and Bush AND Ross Perot. Perot got 20% of populous vote but did not win enough delegates o Spatial proximity theory of voting: voters vote for the candidate “closest” to them ideologically  2 major parties may be centrist/moderate —“converge on the median voter”  Median voter: half electorate is to the right ideologically and half is the left  Does the US have moderate, centrist parties Not really, why o Primaries o Directional voting and not spatial proximity  Madison hopes resurfaced in academic political science of 1950s and 1960s in optimistic form: o Pluralist model/theory of democracy (pluralism): public policy is product of many competing interests  Interest groups are pressuring government and providing support for government  government making public policy  Government as referee in group struggle  Pluralists think this system works best and represents interests across society  good public polity o Assumptions of model  1. All relevant interests are represented  2. Everyone joins and is active in groups  3. Political power and resources are widely distributed  ARE THESE MET o Schnokschnedier disagrees that this is a good method  Thinks they are making assumptions for this to be true  “Flaw in pluralist heaven is that the heavenly chorus sings with a strong upper class accent” 

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Chapter 5.4, Problem 42 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

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Let W be a two-dimensional subspace of n 3. If Tw: n 3 - n