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Show that the function L defined in Example 8 is a linear transformation

Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill ISBN: 9780132296540 301

Solution for problem 29 Chapter 6.1

Elementary Linear Algebra with Applications | 9th Edition

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Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill

Elementary Linear Algebra with Applications | 9th Edition

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Problem 29

Show that the function L defined in Example 8 is a linear transformation.

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2. TRADE SYSTEM (ITS) •Bilateral system of exchange of goods & services: 2 types of trade: 1. Merchandise trade­ primary goods­raw foods, fuels, fibers, minerals, water; manufactured goods­ anything processed. 2. Service trade­ mostly GN dominated vs GS. •Global trade flows: 1913—> $20 Bill = $55,000/day 2013—> $18.3 Trill = $50 Bill/day happened ^ because now countries are more interconnected •Outsourcing­ 3rd party is being paid to complete a job for the company­ contracting another company. •Offshoring­ sending business abroad. •Restoring­ companies returning back to homeland. •GN Has an Advantage in ITS: because of colonization GN has primary goods (produced by colonies/GS states). —> Post colonization, colonies are not industrialized, so create cash crops (crops explicitly grown for export)­ best products are usually sent offshore, while secondary are kept locally. —> Creates uneven trade advantage of GN & GS. GS countries rely on export, because trading closer, or within the country can be costly because of poverty and lack of infrastructure which makes transportation costly. •World Trade Organization (WTO)­ 1995­ creates free trade, opening up as many markets as possible­ easier for GN vs GS­ bigger economy means more leverage. •How States Trade: Multilateral­ Free Trade Agreements (FTAs) ­ NAFTA, APEC, proposed TPP ­ some countries tried protecting themselves from unfair trade/protectionism­ by setting limits on foreign import, such as limiting numbers of cars coming in, which would force consumers to still buy locally made brands. ­ Challenges: since so many countries participate, there is always a loser/unfair advantages/etc. To set limits is also hard, because WTO is having trouble getting all countries to agree to the same contract.­ took 12 years for the most recent agreement. ­ Dispute mechanism­ provided service that rules on cases regarding trade between countries. ­ Recent ruling: #1. U.S. wrongly imposed tariffs on steel from India & China. #2. U.S. wins complaint against Chinese tariffs on U.S. cars. 3. THE INTERNATIONAL INVESTMENT & FINANCE •Int’l Finance­ countries’ checking accounts­ debit & credit. Int’l Investment­ funds invested abroad 2 ways: #1 Foreign Direct Investment (FDI)­ direct money sent by the government or controlling assets (such as money or anything w/value). #2 Foreign Portfolio Investment (FPI)­ stocks, bonds, earned dividends; all is invested by individuals and companies, not the government. •Interdependent: FDI & FPI investments after WW2­ investing to rebuild countries affected by the war ­ investments aren't evenly distributed, so some counties have more say in decisions. •GN Domination: Post WW2 U.S. hegemony (domination). Today: top 500 NNCs—> top 1 is Walmart, otherwise, mostly petroleum dominated. •Gross Corporate Product (GCP)­ needs access to reach more states/be more spread­out. *** Side note: Taxing foreign cars makes them more expensive than domestic, which makes domestic cars more desirable. *** NOTES. PART 2. ECONOMIC SANCTIONS • Economic Sanctions­ actions taken by countries against others for specific economic reasons. • Policies used by countries to change company’s policies or another country’s policies: boycotts, freezing banking assets, etc. Ex: IMS, ITS, II. • Political sanctions­ ex: limiting incoming immigrants from specific countries. • Effectiveness of economic/political sanctions are as effective as the countries applying sanctions. Usually rarely effective, but makes a statement. ­Ex: EU & U.S. against Russia; U.S. vs Cuba­ embargo/shutting down supply income during Cold War, to prevent a nuclear strike. Iran­ oil blocked due to nuclear weapons programs. ­Diplomacy­ foreign relations between countries; need to be sovereign countries to engage in diplomacy. Diplomacy is usually recognized with an establishment of an embassy (or embassies)­ a piece of land governed under its own country’s government, where visas are given and where support of its own citizens is given on that foreign land. Objective to diplomacy: promoting & preserving self­interest. • GN countries usually have more leverage vs GS, because are usually stable and older/more established. • Modern era of diplomacy begins­ Treaty of Versailles, 1919. • Who is involved in diplomatic affairs: 1. Head of govn’t (the person in charge of the whole govn’t)­ president, prime minister, chancellor, premier, etc. 2. Head of representative of country’s foreign affairs office­ secretary of state, minister of state, etc. 3. Ambassadors­ whoever is appointed to the position in charge of an embassy. 4. Civil servants­ foreign service officers working in embassies (also send information about the country back home). NEGOTIATION ENVIRONMENTS 1. Hostile Diplomacy­ armed or potentially armed conflict­ ex: N. Korea article. 2. Adversarial Diplomacy­ little chance of armed conflict­ ex: Solar Panels article­ U.S. & China. 3. Coalition Diplomacy­ cooperation to solve issue (a group of countries involved)­ ex: Killer Deal article­ Arms Trade Treaty. 4. Mediation Diplomacy­ third party helps in a stalemate between two other countries­ ex: Peace Talks Bids article­ U.S. intervenes w/Palestine & Israel. • Other ex: ­Kashmir­ hostile diplomacy. ­Outer space issues­ coalition diplomacy. ­Ukraine v Crimea­ hostile diplomacy. ­Indonesia fisheries­ coalition diplomacy­ could also be adversarial diplomacy. ­Preserving MPAs (Marine Protected Areas)­ coalition diplomacy. ­Cuban Missiles Crisis­ hostile diplomacy. • States & Negotiating Power: 2 level games: both Int’l & Domestic factors are involved. 1st level (international): 2 or more states are involved in negotiations. 2nd level (domestic): negotiations are discussed by the domestic population (the people) and diplomats. *** Side note: if at a 2nd level, people don't agree with the changes, the changes wont occur. Even if the laws change, if people wont obey them, or go against the government, the policy/change wont be effective. This is why BOTH levels are crucially important in negotiations. *** Ex: Eurozone Crisis­ 1st level (international): Greece and Germany negotiate a deal where Germany will have to bail Greece out of its financial crisis. 2nd level (domestic): Germans are upset because their tax dollars are going to Greece/upset because they have to bail Greece out of financial crisis. Greeks are upset because now they have to pay taxes they have never paid before, so that the government can use that money to pay back Germany for its help. SECURITY & COOPERATION 21st century security issues: • 9/11, 2001. • War on Terror (Bush administration)­ going into Afghanistan in 2001/Iraq 2003­ landing troops to control the situation & capture Osama Bin Ladin. • North Korea­ concerns over missile launches­ yearly tests. UN Resolution 2270 (passed 3.2.16). China is in a sensitive spot, because it shares a border with North Korea; also trades­ luxurious items that only top 5% of North Korea has, the top that controls the country. • Arab Spring 2011­ civil uprisings demanding changes in govn’t­ fight dictatorship. Syria­ most serious situation­ Assad regime­ claims he has been democratically elected, but his family has been in power for many years. The conflict began out of World Recession, that caused food shortages, financial struggles, unemployment—> led to Arab Spring. Libya­ conflict over several governments­ which will rule. Egypt­ the government is afraid of protests, so people are arrested for walking on the street in groups of larger than 4. Tunisia­ Arab Spring turned out in a new better government, but economic struggles still exist and terrorist groups are hurting tourism. • Jihadism­ “struggle” unite Islamic faith Appeasement Policy—> gave Sudetenland to Hitler (the land he was fighting for). Reasons: avoid another war; the land was surrounded by Germany geographically; countries could not afford another war economically; Germany was a buffer from the spreading Soviet Union, so countries were hoping if Germany gets what it wants, it will protect them from a conflict with Soviet Union. Why is Baltic situation comparable to the Sudetenland situation • Native speaking Russians: Estonia=25%; Latvia=27%; Lithuania=6%. • Baltic states fear annexation by Russia to protect “local” population. • Want EU and NATO to do more­ want tougher sanctions; but reliant on trade w/Russia, especially gas supply (need an alternative). INCREASE IN ARMS TRANSFER • Cold War= arms race. Post Cold War­ a lot of weapons left, but countries cannot let the businesses go out of business (bad for economy), so they exported weapons to other countries = more weapons in circulation. • UNSC P5 + 1 ==> P5: U.S., Russia, China, France, UK. & +1: Germany. • UN ATT proposal­ attempt to control weapons & preserve peace. INCREASE IN SEVERITY: TECHNOLOGY Cluster bombs: Fist the canister released from the aircraft (1,000 lb). Then, the spinning canister opens and 200 bomblets are released. Finally, the individual bomblets float down to target (length­ 8in) and break into small metal­like fragments. Pros: massive killings, less of your troops dead. Cons: massive destructions, hostility. • Change in focus of security: guns & bombs—> human security concern. Now, instead of trying to get rid of weapons, countries realized they should focus on human relations & improvement of lives. • Increase in frequency: Decolonization­ countries still cannot support themselves. Civil unrest­ domestic conflicts­ usually countries that were decolonized earlier experience less civil unrest today vs those decolonized more recently. CONSEQUENCES OF CONFLICT: SYRIA • More than 4 Mill have fled Syria.­ most went to neighboring countries (mostly Turkey).­ 66,000 fled to Turkey in one day. • Int’l Consequences: ­spill­over effect­ conflict spilling over into other countries. ­creates hostilities­ within the country, within other countries, between countries. ­interference w/trade­ oil, tomatoes, etc.­ prices rise­ other countries suffer through trade. ­forestalls development­ before Syria had an emerging economy; now its in ruins; this is also destabilizing other countries’ economies as well. ­emigration­ refugees. ­intervention issues­ when to intervene, if intervention is right, what to do, etc. At first, the conflict was domestic, so UN didn't want to get involved. THREAT • Int’l terrorism­ to instill terror in civilians. • Reaction to perceived threat: colonization, westernization. • State­sponsored terrorism­ govn’t inflicting terrorist attacks. Ex: Rwanda (Tutsi) —> M23 Congo rebels. Iran (Shia) —> Hezbollah, Houthis. • Objectives of domestic terrorism: attention, challenge govn’t, independence. Freedom fighters vs terrorists­ relative concept, but very unclear.

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Chapter 6.1, Problem 29 is Solved
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Textbook: Elementary Linear Algebra with Applications
Edition: 9
Author: Bernard Kolman David Hill
ISBN: 9780132296540

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Show that the function L defined in Example 8 is a linear transformation