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# Let L: P3 -+ P3 be defined by L (lIf3 + bf2 + cf + d ) = 3ar 2 + 2bl + c. Find the

ISBN: 9780132296540 301

## Solution for problem 15 Chapter 6.6

Elementary Linear Algebra with Applications | 9th Edition

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Elementary Linear Algebra with Applications | 9th Edition

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Problem 15

Let L: P3 -+ P3 be defined by L (lIf3 + bf2 + cf + d ) = 3ar 2 + 2bl + c. Find the matrix of L with respect to the basis S={t3.1 2. 1.ljforP3.

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Unit 2 3/21/16  Presidential Reconstruction 1865-1867  Congressional Reconstruction 1867-1877  Three Elements of Reconstruction  Economic  Political  Racial  Freedmen  Aren’t slaves anymore, but aren’t necessarily citizens  Legally they are, however they generally aren’t accepted as such  Rooted in the purpose of the Civil War  South had just finished fighting for 4 years to protect the idea of white supremacy  White Supremacy: “The Organic Law of the Land”  White Supremacy Factors  Scientific racism  Phrenology  Crainometry  Intelligence = IQ tests  These tests were often extremely biased  Eugenics  Social Darwinism: “Survival of the fittest”  Laissez-faire: economics and government: allows natural order of things  Self-reliance  “rugged individualism”  Honor  Localism  Tradition and violence flourish  New South Creed  Progress thru uniformity  Savage Ideal  Conformity thru violence  The mindset to maintain white supremacy by any means necessary  Southern Rape Complex  Sexual threat to white women  Any threat of change that a black made against the social structure was a threat to white women  There was a common stereotype that black men raped white women (untrue)  Edgefield Policy  Savage ideal in action  Gave white men the responsibility to do whatever is necessary to maintain control in the black population  Racial Violence Lynching  1880’s-1910’s  Killing off black elected officials  Occurred once every two and a half days  Nadir: 1880-1920  Legalized discrimination every southern state by 1910  2,000 African American elected and appointed to office in South from 1867 to 1900  Whites dominated Reconstruction in almost every way  But, biracial government functioned in South for a time  Blacks and black legislators had helped significantly in setting the country back on the right track, but were rewarded with discrimination  South Carolina had 39 black legislators in 1877, zero in 1900  Result of Jim Crow Laws  Mississippi Plan  Adopted by a state constitutional convention in 1890 th th  Attempt to circumvent 14 and 15 amendments  Residency requirement  6 years  Then entitled to register  Poll tax: \$2  Literacy test  Understanding test  Grandfather clause  White Democratic Primary  Segregation  Plessy v. Ferguson 1896  Validated “Equal and separate”/separate but equal  Mississippi v. Williams  Validated Mississippi Plan  3 Great Forces  Industrialization  America becomes an industrial giant  Agrarian turned into industrial  Urbanization  Highest standard of living in human history  Political, economic and social power shifted from countryside to the city  Immigration  Became truly a multi-cultural, pluralistic, diverse society  Iron Age of American history  Spurred by the Civil War  Post-Civil War  Exports 3x  Population 2x  Standard of living 2x  Railroads key factor  Industries based in or near cities, or industrial towns  Led to large corporations and monopolies  Revolution – industrial capitalism rises to absolute power  Industry is developed in Urban Centers  Centrifugal force of industrialization expanded industrialism and the power of businessmen everywhere  The businessman vied with the cowboy as the quintessential American  The businessman overwhelmed the farmer in wealth, political power and social status  Centripetal force brought more people into centers from which power radiated – cities  Created metropolitan areas  Urban America  Industrialization created cities and gave them a new and alien character, fueled by immigration  A small percentage of the population became extremely wealthy  Population went from 6 million to 44 million  Robber Barons  Political machines and corrupt political bosses  Chaos, crime, consumption  Huge foreign-born population  Immigration  Greatest voluntary migration in human history  Pre-Civil War Immigration  British, western European, Northern European, African, Hispanic, Asia  New Immigrant stock  Central Europe, Southern Europe, Eastern Europe/Russia, Asia  Religion among immigrant shifted from protestant to Roman Catholic, Eastern Orthodox, Jewish, Buddhist, Confuscian  Motives for migration  Push factors  Land consolidation  Commercial farming  Industrialization  Religious and political persecution  Often applied to Russian Jews  Pull Factors  Higher wages  Higher standard of living  Better Opportunity  More freedom  Often considered to be temporary migration  The Melting Pot  Cities largely foreign-born  Ethnic enclaves developed like Little Italy, Five Points, Chinatown  Meanwhile, the countryside was populated more by native- born  Xenophobia  Fear, dislike of foreigners; often irrational  Nativism  Policy or ideology of protecting native inhabitants, indigenous culture, etc., against immigrants and foreign influence  A natural born citizen  A citizen from birth by place of birth (or by descent); doesn’t need naturalization  Native born  A person born of a citizen of the U.S.; doesn’t need naturalization  Naturalized citizen  A person who has become a US citizen as opposed to being born as a US citizen 

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Let L: P3 -+ P3 be defined by L (lIf3 + bf2 + cf + d ) = 3ar 2 + 2bl + c. Find the