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Solved: In Exercises 21- 28, a linear operator Ton n is

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

Solution for problem 25 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 25

In Exercises 21- 28, a linear operator Ton n is given. Find, if possible. a basis B for 'R" such thar 25 [T ]

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Step 1 of 3

Notes Wednesday, August 26, 2015 9:03 AM Sociology and the Sociological perspective What is sociology -The systematic study of human societies  We study the social context in which we live because we are social beings more so than we are individuals -Developing a sociological perspective  Recognize that our daily lives reflect a complex interconnection of social forces and personal characteristics -Sociological Imagination  The ability to think systematically about how things we experience as personal problems are really social issues  Think about how war, unemployment, obesity are both personal problems and social issues  The hallmark of the sociological imagination is being able to ask HARD questions and not settle for easy answers -Trying to understand the World Around Us  How do know what we know and how do we make sense of it all  Answers arrived at through facts and theory  Facts  Scientific explanations that have been tested and confirmed so many times, they don't need to be tested anymore  Theory  Explanation about relationship between individuals and society, that is supported by evidence  Paradigms- scientific and/or philosophical frameworks or models for explaining social phenomena The Functionalist Paradigm  Society is a whole unit made up of interrelated parts that work together  Social order maintained through consensus  We all in this together and we just one big unit.  We're made up of systems  Education system, economic system, etc  To understand society, we need to examine the structure and function of each part  Why do we need this specific system/ function What does it do for society  Types of Functions (Robert Merton, 1968)  Manifest- intended functions that contribute to society  Specific goals, college wants to specifically get us a degree, a better job, knowledge  Latent- unintended functions contributing to society  Things that unintendedly happens. In college you will make friends, and might meet your future spouse but that isn't part of a college's goal  Dysfunctions- unintended negative consequences  Bad things that happen, that we didn't intended  In college: debt, stress, alcohol/drugs  Key question: What is the benefit or function for society August Comte (1798-1857)  Pioneer of sociology  First to attempt to create a "science of sociology"- called positivism  If we can understand how people live together peacefully and successfully, then maybe we can fix our society (he was living in the French revolution)  Purpose: learn how society works (functions) so we can make it better  Social engineering Herbert Spencer (1820-1903)  Proposed functional theory of evolution of societies  He was influenced by Charles Darwin  Society is like a living organism  There are interrelated parts that evolve from lower, simple forms (barbarian) to higher, more complex (civilized) forms  Society evolves, they try new things and change  Social change occurs through process he called "Social Darwinism"  Coined the term "survival of the fittest" Emile Durkheim (1858-1917)  Identified the role of social forces and group influence/membership  Social facts- characteristics of group beyond summary of individuals  Society is influenced by groups  Groups have influence beyond the aggregation of their members  Social order is maintained through consensus and solidarity (belonging together)  Social integration vs anomie  We as a society are strongest when we are integrated  Suicide example  He was interested in suicide rates, different groups have different rates of suicide Groups have a profound influence of how we view ourselves The Conflict Paradigm  Society is best characterized as being composed of groups that are in conflicts with each other over scarce resources  Conflict between groups and individuals primarily shapes and society  Social order maintained through economic interests and the exercise of power by some groups  Social class is an important group in the competition  Key question: Which groups benefit from the way society is organized Karl Marx (1818- 1883)  Economic determinism- all aspects of society reflect economic system.  Importance of Social Classes- Bourgeoisie (owners) & proletariat (workers)  Determined by who controls the means of production  Bourgeoisie owned LAND, and on the land you could have factories, so they had the most valuable possessions, they own  Proletariat is everyone else, they have to work  Class consciousness and class conflict  An awareness of one's (and other's) common relationships to the means of production.  Conflict occurs when different "classes" compete for the same things  "false consciousness"- workers adopt and endorse the consciousness of the owners as "right" Max Weber  Debated Marx on singular role of economics in determining what society looks like  Power is not always linked to economics  Rise of the rational society  Transformation from tradition to rational  McDonaldization of Society (Ritzer) Symbolic Interactionism  Society is composed of symbols that people use to establish meaning, develop their attitudes and beliefs and communicate 8/28/2015 8/28/2015 9/4/2015 In a functionalist perspective  Social order is maintained by following the rules set In Conflict theory perspective  Social order is maintained by someone of higher power being in control Symbolic interaction  Social order is maintained through our interactions, common understanding, and agreements  Social order grows of how we define symbols, ourselves, relationships with others, events etc.  Important concept is social construction of reality  Reality varies depending on social context  The definition of the situation  W.I. Thomas Theorem- "if (men) define situations as real, then they are real in their consequences" Feminist Social Theory  Placed gender and gender inequality at the center of its theoretical lens  Challenged many of the presuppositions of classical social theory for its male-centered biases 9/9/2015 Producing Knowledge -Three basic questions:  How do we know what we know  Use of social science methodologies  Science of the obvious vs. "myth busters"  Why does it matter  Why is it important  Research informs us and protects us  What's next  Research frequently points to policy implications Basic Stages of Sociological Research -Identify what it is we want to ask or study  This is one of the hardest parts of research -Figure out the best methods of tools to address the question -Collect and analyze date in search for answers -hypothesis  The tentative prediction we have about what we are going to discover before we begin the research can be studied given the limits feasible questions of times resources steads to think more specifically about a topic sheets to turn ideas about a topic into a working hypothesis 9/11/2015 General Research Guidelines -social research should generally be systematic, not anecdotal  Systematic is more specific, and anecdotal are little stories -Research should produce evidence that is empirical -conclusions/interpretations are generally BEST understood in terms of probabilities How do we know what we know 2 Basic categories of research methods 1 Quantitative -deals with numbers, statistics -uses surveys  Good for getting information on large numbers of people -Experiments  Use of experimental group and control group  Good for "cause and effect" but hard to imitate in "natural settings" -Secondary Analysis  Use of date (government collects a lot) that have already been collected 1 Qualitative Research -specifics, quality -uses Interviews  Great in-depth information, but hard to generalize -Participant Observation  Researcher becomes a member of the group being studied -unobtrusive (nonparticipant) observation  Researcher studies (observes) without making others aware  Laud Humphrey's "Tea-Room Trade"  Tea rooms are public rest rooms where gay men have anonymous sex  Stood at a Tea-Room and became the watch queen, he wrote down everyone's license plate number to figure out what kind of people go to Tea-Rooms 1 Ethical Standards for Sociological Research American Sociological Association (ASA) has created six ethical standards to guide sociologists' professional and research responsibilities and conduct 1 Professional and Scientific Standard 2 Competence 3 Conflicts of Interest 4 Research Planning, Implementation, Dissemination 5 Informed Consent and Confidentiality (protection of research) Society and Culture 1 Society A system of interrelationships that connect individuals together  Lives are a collection of encounters, conversations, interactions, etc  Society is the sum of all things, how they are related and how they are organized 2 Culture The most pervasive part of any society Significance of culture is MOST evident when you are in someone else's Culture defines and describes shared human social parts  The nonmaterial marts (language, beliefs, values, norms, behaviors) of social life, and material objects (artifacts) that are passed from one generation to the next 3 Language  Language is one of the most important sets of symbols with culture and society  It enables creation of culture through communication of shared meanings  Sapir-Whorf Hypothesis of Linguistic Relativity  Language helps determining how reality is constructed  Realities vary from culture to culture in part because language varies from culture to culture 4 Cultural Values  Values are socially-constructed ideas about what is generally considered desirable or valuable  Although there is great diversity in societies, most have dominant values- adopted by the greatest number of people 5 Norms  Culturally-defined rules of behavior  Norms vary in seriousness  Folkways- informal norms or customs  Elevator norms, walking on the right side of hallway  Mores (Mor-ays)- Formalized norms, often codified into law  Don't take food off other people's plates, don't steal Taboos- Very serious norms, often prohibited   Sexual assault, incest,  Culture as a reference point  We rend to believe that our own culture is "normal" the "lens" through which we perceive and evaluate our surroundings  Ethnocentrism  Belief in superiority of own culture  Cultural Relativism  Judgement based on culture's own perspective Cultural diversity  Subcultures  Part of the larger culture, but with important distinctions  Countercultures  Subculture that is intentionally opposed to the larger culture "Teaching" culture  Socialization  The process of teaching and learning society's norms values, roles, etc., to new members of society  Training people to "behave appropriately"  Life-long process  Change circumstances may require re-socialization  Learning new norms, values, attitudes, etc.  Re-socialization occurs to the greatest extent in places called total institutions Teaching Culture  Socialization- teaching and learning society's norms, values, roles, etc. to new members of society  Train to be trained appropriately Lifelong process  Changing circumstances may require "re-socialization"  Can be extreme called a "total instatution" Agents of Socialization Teaches the rules of society  Families, habit formation  Families with infants will put us in formation as eating and sleeping information Peers  Importance of reference groups --> compare them Education  "hidden curriculum" --> what you learn that is not in the academic curriculum Media  Power of advertising Religion  Morals, right and wrong Socialization and Self  Self-aware--> becoming to know who we are  Self- the sum total of our conscious perceptions of how our identity is distant from others  We always change who we think we are throughout life Cooley "Looking Glass Self" Social Structure and Social Interaction  Social structure  Recognizable regularities or patterns in society  Particularly in regards to social relationships  It provides framework or organization of society and makes living in societies somewhat "predictable" (predictable pattern, the social norms)  Parts of Social structure: Status  Status= position in society  Students, daughter, children, lifeguard  Ascribed status= assigned statuses  Gender, daughter, race, age  Achieved status- earned or chosen statuses  Job, college student, financial worth  Status symbol  Material items used to communicate out statuses  Babies, you symbolize a boy with blue and a girl with pink or a bow  Wedding rings  Conspicuous consumption- consuming material things with the intent of communicating status superiority  Fancy clothes, jewelry, brand names  Status inconsistency  When two statuses are incompatible  Roles  Are the expectations and behaviors that accompany status  Role performance  Role conflict- conflict between roles associated with two of different statuses  In a sorority and a student  Have to work on the homecoming float but have to do your homework too  Role strain- strain created when two roles within the same status don't fit well  Role playing- social interaction  Dramaturgy: Irving Goffman  Life is like a drama in which we regularly role-play  We create how we want others to perceive us through a process called impression management  We use props and lines "sell" images of ourselves to our perceived audiences  Face- positive social identities we wish to claim  Tact- helping others "save face" Notes Wednesday, September 30, 2015 9:17 AM Social Control, Deviance, and Crime Groups pressure: conformity  Belonging to groups puts significant pressure on members to conform  The Asch Experiment  The test with lines, length of the lines  People would say the wrong answer if the rest of the group said the wrong answer  Informational conformity  You genuinely think you must be wrong because everyone else's answer was different from yours.  Normative conformity  When you know you're right but you still give the wrong answer so conform to the group so there's no awkward situations  When conformity goes too far there is a risk of "groupthink"  Pressure to agree overpowers individual members' willingness to weigh alternatives  Collective tunnel vision Social Control  Despite individual role performances, societies must have conformity and predictability from its members  Social control- mechanisms for ensuring conformity and maintaining social order  Informal social control  Reactions (unofficial) of peers and others that encourage conformity to rules of norms  Internalization-- we learn (socialization) and adopt acceptable behaviors  Formal social control  Official authorities enforce rules and laws and often apply official sanctions to deviance Deviance  Deviance refers to people whose behaviors, beliefs, and/or appearance fall outside of the "normal" range of social expectations  Social scientists generally reserve the term deviance for violations of significant social expectations  Anything that goes against the norm is deviant  Important of negative reactions  Stigma --> extreme social disapproval (a mark of disgrace) because of some personal characteristic  Absolute deviance vs relative deviance  Ideas about deviance change with time, place, and culture Criminal Deviance  Some deviance is serious enough to called crime  Crimes are acts that violate criminal laws or statues  Big questions  How much crime is there  Who commits crime How much crime is there  Two major sources of violent and property crime date  FBI- Uniform Crime Report  Crimes reported to law enforcement  Department of justice - National Crime Victimization Survey  Survey that finds more crime (about 2-3 times more)  Most violent states  Tennessee  California  New York  Rates take into consideration population differences  Crime rates are decreasing  Murder rate is less than 1/2 what it was 20 years ago Who commits crimes  Profiling  Age  Young people are more likely to commit crimes than old people  15-24  Sex  Males are much more likely than woman  Race  White more (because there are more white people), but blacks and Hispanics are more likely (compared by rate)  In America, almost all crimes are INTRA-RACIAL  Racial profiling  Using race as a measure on whether or not someone should be a suspect Exercising Control with Deviance and Crime  The criminal justice system- formal control institutions and processes that enforce criminal law  4 purposes of punishment 1. Incapacitation (incarceration is primary form)  Death penalty is another form 2. Rehabilitation  Fix you, make them a better person 3. Deterrence  use punishment to discourage criminality and future crimes 4. Retribution  Revenge, pay back. Pay for your crimes  Recidivism rates- measure effectiveness of CJS Functions of Deviance 1 Promotion of conformity and unity  gives us social norms  Comparison of how not to behave 2 Clarification of moral boundaries  Abortion 3 Jobs and services to deviants  Police, corrections, social workers 4 Social change  Rosa Parks Conflict Perspective on Deviance  Deviance and definitions of morality/immorality reflect power imbalances  Unethical, harmful, and/or immoral behavior exists at all levels of society, but tends to be criminalized for the less powerful  Business owners harm society but don't get arrested  In conflicts between groups, some groups do a better job of making their "definitions of what is deviance" stick *Damp Social Stratification 1 Social Differentiation  Categorize or group people based on different physical or social characteristics 2 Social Stratification  Systems of ranking socially-differentiated people or groups How are people stratified  Social scientists use 3 basic characteristics to try to measure stratification 1. Prestige  Status, respect/admiration attached to a social status  Occupation is key 2. Power  The ability to get others to do what you want, even if they don't want to  Coercion v authority Form of authority- Max Weber  Charismatic  Power arises from leader's personal characteristics  Traditional  Power rooted in custom 1 Economic resources  Wealth, and income Wealth- net value of the assets you own, real estate, financial assets (stocks, bonds) Income- receipt of money or goods over a particular accounting period Wealth/income distribution  How much does one need to own/earn to be considered rich  Wealth distribution (inequality) What about income in the US  Median household income in the US of 2013 is $51,017  Income trends  Highest paying jobs Why is there inequality  How should society determine who gets how much  Functionalism (Davis and Moore)  Some position (jobs) are more important that others  People vary in skills, ability, and competence  How do we motivate competent, able people to fill important positions  Higher incentives (pay, prestige, power) encourage competent people to take more important jobs  Conflict theory and stratification  Inequality reflects power balances, and those with more power use their advantages to maintain their elite status  Resources are not distributed evenly. Incentive differences are not the only explanation for income and wealth inequality  Conflict perspective  Wealth flows upwards  Exploitation- trying to minimize the costs of labor- "the less you pay, the greater your profit"  Robert Reich: American capitalism is a history of the struggle over wages Defining Social Class Class and inequality  Social classes are people who share similar economic situations  Conflicting economic interests with other cases  Similar life chances  Similar attitudes and behaviors American Social Class Structure (1 of 3) Upper class  Possess significant income/wealth  For many, income is not job-related  Importance of inheritance and proper upbringing  (nouvou riche VS old money)  Highly educated at elite institutions  Not necessary for employment Middle class  Adequate to substantial income. Less wealth  Income is primarily employment-based  Wealthy largely held in retirement- style accounts  Education is important determinant of employment  Upper-middle class among most highly educated (post-graduate)  Education more likely at state/public universities  Job security with benefits (better at top than bottom)  More likely to be salary labor Life at the bottom Terms  Absolute poverty  Poverty line  A guesstimate of how much money a family needs to live, a basic minimum line  Official Federal measure (Census Bureau) since 1963  Poverty based on pre-tax, gross income thresholds that vary by family size and composition  Formula: 3 times the cost of a "minimum food diet"  2013 Data  Threshold for family of 4 was $24,000  Relative poverty  You might make more than the poverty line, but your life still isn't that good  Poverty risk factors  Education  Employment  Minority  Age  Family structure  The average people who live under the absolute poverty line: 45.3 million Functionalist  Functions of Poverty  Economic functions  Labor force for society's "dirty work"  Subsidize activities for affluent  Created jobs for services to poor  Outlet for undesirable goods  Being poor means never owning clothes that weren't owned by someone else first  Social functions  Help uphold legitimacy of conventional norms  Helps guarantee status of non-poor Conflict theory  Poverty is "functional" for capitalists because it provides exploitable labor  Culture of poverty  Norms and values unique to poverty subculture are passed on across generations  Eg., inability to "delay gratification"  Being poor is feeling helpless when your child makes the same mistakes you did, and won't listen to you beg them against doing so Misconceptions about poverty 1 Poor people are lazy  Most poor adults have jobs or they are too young, too old, or disabled 2 Welfare Dependence  1996 Personal Responsibility and Work Opportunity Reconciliation Act 3 Most poor are Chronically Poor  Majority of poor are temporarily poor, although many live very close to the line (<10% are poor for 3 consecutive years)  People who are unstable are more likely to be poor, but poverty also tends to makes people unstable Social Mobility Types of mobility 1 Intergenerational mobility- compares adults with parents 2 Intergenerational mobility- compares adults at beginning of career with end of career Importance of college education- is particularly acute for people at the bottom of the class structure Race and ethnicity Does race matter  Race is a socially-constructed idea that refers to people are share selected physical characteristics that are given social meaning 1. Race is an invented classification system Humans are 99.9% identical at genetic level 1 Race is socially created There is little or no scientific agreement on a biological basis for race. PERCEPTION is key 1 Ideas about what racial groups change with time and across societies The basics: Ethnicity  Ethnicity is based on shared cultural and social characteristics  Nationality and religion are often connected with ethnicity  Ethnic groups tend to have unique/ distinct beliefs, values and behaviors  Shared sense of identity and therefore a shared sense of belonging Census Bureau and Race/ Ethnicity  2000 Census first year that allowed respondents to identify with more than one race Race/ethnicity  Median household income  Other measures of well-being  Infant mortality  Life expectancy Racism- two phenomena Prejudice  Negative beliefs or attitudes held about entire group  Broadly applied, subjective, and stereotype-filled Racial Discrimination Forms  Using negative words or phrases in reference to particular group  Placing limits on opportunities based on racial group membership  Engaging in violent acts against an individual or member of a racial group Classifications  Individual discrimination  e.g. RaceCard Project "Don't bring a black man home"  Institutional or structural discrimination -- embedded in social institutions  e.g. Voting rights (blacks-- 18866 and women 1914), military segregation  Tyson Video Racism in Post-Civil Rights Era Evidence of racism today  2012, found that "explicitly anti-black" attitudes among votes increased after election of President Obama  Surveys of whites suggest that "stereotypical blacks" are perceived to be more criminal  2014, found that harsher punishment are more acceptable when offenders are perceived to be black  Surveys of whites suggest that "stereotypical blacks" are perceived to be more criminal  Public support for voter id restrictions increases when images of non-white voters are presented Privilege  Social, cultural, and economic advantages associated with membership in a particular group  Tendency to view these advantages as "the norm" for all and are therefore often not recognized as advantages  Doesn't mean privileged group doesn't have to work hard, they just don't face some of the same obstacles  e.g., name association experiment Think about forms of privilege  All of the following are determined by birth:  Citizenship  Social class  Sexual orientation  Sex/gender  Abilities v. disabilities  Race Racial/ ethnic co-existence  Assimilation-based relations  Anglo-conformity- immigrants are accepted as long as they conform to the host society. Traditional American institutions are maintains  Melting-pot- all ethnic and racial minorities blend together  Cultural pluralism- recognizes immigrants desires to maintain at least a remnant of their "old" way while accommodating American values and norms Conflict in Co-existence  Segregation- physical and institutional separation (forced or voluntary) of dominant and minority groups  De jure segregation (legal) & de facto segregation  Sub segregation- involuntary social separation with unequal rights (slavery)  Expulsion0 forced removal of one population by another Overview of Genocide  Genocide- the intentional extermination of one population by another  Genocide in the past 100 years  Armenian  Holocaust  Cambodia  Bosnia  Rwanda  Kosovo  Darfur Sex and Gender  Sex and gender tend to conceptualized as two-category, mutually exclusive groups: male and female  Sex  Determined by largely visible biological characteristics like primary and secondary sex characteristics  Gender  Socio-cultural characteristics and expectations that includes ideas about masculinity and femininity  Women in Positions of Power  Government  Presidents- 0  114th Congress: Senate- 2 (20%) and House- 84 (19%)  Supreme Court- 3 (33%)  Governors- 6 (12%)  Business World  Fortune 500 CEO's (5.2%) Fortune 1000 (5.4%)  Sports  Coaches of women's sports- (40%)  Concepts relating to Gender  Gender roles and norms  How do women and men "behave" differently  Culturally-based expectations associated with each gender  Gender identity  Sense of self as being male and female and masculine or feminine  Transitions of Women's roles  Three historical waves of feminist movements  First (late 19th century)- emerged as part of flight against slavery  Produced the 19th amendment  Second (50s-70s) questioned traditional roles of men and women  Third- is one going  Women should be able to choose roles (traditional or new)  Gender stratification  Differential rankings based on sex  Why is it okay for girls to look like boys (e.g. short hair, jeans, etc) but not okay for boys to look like girls  Sexism  Beliefs that one is sex is inferior used to justify inequality and discrimination  e.g., technology and pre-birth sex- selection  Economic inequality by gender  The pay gap  Appears within first year out of college, even when women outperform male counterparts in college  Women are paid less because the boss thinks they may decide to have a family Discrimination  Any behavior that harms individuals or puts them at a disadvantage on the basis of their group membership  Maintains social hierarchy by blocking advancement of subordinate groups Notes Monday, November 02, 2015 9:14 AM Marriage and Family Questions of definition  Marriage and family are social constructs of meanings and relationships  What is marriage  Legal union based on mutual rights and obligations  What is a family  Two or more people who are related by blood, marriage or adoption  Household-- people who occupy the same housing unit General Rules of Mate Selection  How do we choose our mates  Exogamy & Endogamy (within group)  Religion and race  Homogamy  We tend to marry people who are like us  Social status, class  Propinquity- social nearness  Matching hypothesis  Physical attractiveness categories  Look for partners within our categories  Out of your league  Exchange theory  Maximize personal benefits  Notable rise in "earning potential for both men and women"  Monogamy (serial) Patterns in intermarriage  24% of black males, but only 9% of black females married non-blacks  17% of Asians males married outside their group  36% of Asian females  Intermarriage rates for whites and Hispanics did not vary by gender Why marry  Married people are happier, healthier and better off financially  Married couples:  Enjoy higher standard of living relative to unmarried people  Report higher levels of well-being and life satisfaction  Healthier lives  Report more frequent and fulfilling sexual activity  Children in two-parent households:  Enjoy higher standard of living  Tend to perform better in school that children from single-parents households Variations on the American Family  Traditional Families  Two parents, one "bread winner" with children  Account for less than 10% of families in U.S.  Age at first marriage is increasing  Women now at 27, men at 29  Affects both fertility rates and divorce rates  Re-constituted (step) families  Gay/Lesbian families  <1% of US households, but up to 80% since 2000 Family Variations- Unmarried options  Marriage rate have decline to lowest levels recorded  Over half of American adults are unmarried (51%), compared to 72% married in 1960. the majority of Americans NO are NOT married  Remaining single  Significant increases, especially for women  Single-parent families  Only about 65% of children in US grow up with both biological parents Out-of-wedlock births  What % of babies are born to single mothers  Overall percentage is 40.8%  Age- teens account for about 1 in 5 out of wedlock births, down from 1 to 3 in 2000  Single parenthood by race/ethnicity  Asians- 17%  Whites- 29%  Hispanics- 53%  Native Americans- 66%  Blacks- 73% Cohabitation  Living with someone you're not married to but in a relationship with  Rates have increased, especially since recession  Majority of people in their 20s will cohabit at least once  Majority of all marriages will be preceded by cohabitation  Why  2/3 of young adults surveyed believe that cohabitation is a good way to avoid divorce, although standards are different  Most occur through processes of "slide, not decided"- cheap, convenient, quick decision  Getting in is easy, exiting much harder- "consumer lock in" Perspectives on Marriage and Family  Functionalism  Reproduction- the "good life"  Replacement level/ fertility level- 2.1  Socialization of children  Economic security/protection  Sexual regulation and the norm of "illegitimacy"  Conflict theory  Family transmits inequality across generations  Gendered roles reinforced within families  Symbolic interactionism  Investigate meanings of roles, changing relationships, etc Divorce  What is the US divorce rate  About 50%.  Marriage= 6.8/1,000; Divorce= 3.6/1,000  2012 Marriage success rates  Rate has been slowly decreasing for 20 years, but still high  Factors related to mid-1900s increases in US rates: Greater tolerance Ease: no fault divorce vs covenant marriage Increased social and economic independence of women • a Test Why does religion exist  Religion is a cultural universal  Most cultures have at least one religion, but you can't find a culture that is areligious  Functionalism  Provides meaning  Provides social unity and belonging  Socialization and social control  Social change  Conflict Theory  Religious has been an important basis for conflict, oppression, and war  Religion reflects and propagates inequality  Religious used to legitimate the status quo, especially by ruling class  Religion is "the sigh of the oppresses creature… the opium of the people" Trends: declining affiliation  Decline in mainline, traditional religious affiliation  First time protestants below 50% in history of surveys  33% of those ages 18-22 are "unaffiliated" compared to 10% of their parents and 5% of their grandparents  68% of unaffiliated adults believe in God, 37% are spiritual but not religious, and 21% pray daily.  U.S. is still a very religious country, by comparison  65% say religion plays significant role in their lives, compared to 33% of British and 11% of French Demographics of Religion in the US  Social class and education have important correlations with religion  Gender  Women are more religious  Females subordination to males is found in the religious texts if all the world's major religions  Race and ethnicity  Blacks report highest levels of religious affiliation  Tend to be protestant  Sunday the most segregated day of the week Civil Religion  Civil religion is a public religious that expresses a strong tie between deity and a culture  Concern over prayer in school, or Pledge of Allegiance or "In God We Trust" on currency  Sense of "religious nationalism"  Belief that nation and institutions sanctified by God  Generic religious (God) references Health and Healthcare Definitions  Health- refers to the extent of a person's physical, mental, and social well-being  Healthcare system- the social institution that seeks to prevent, diagnose, and treat illness and to promote health in its various dimensions  "activities that promote and maintain health" Why talk about health care  Health care system is one of the major institutions in society  All people will interact with this institution at some point in their lives  Healthcare system plays a significant role in well- being. Which is an important point of interest to social scientists  Sociology focus is less about explaining why someone become sick, than addressing the following:  What does it mean to be sick and who decides  Why is disease not experienced evenly across society  How does social position affect health and healthcare experience Functionalism view  Views health problems as dysfunctional in society  Sick people are less able to fulfill role and this society suffers  Societal response is "sick role" - appropriate behavior patterns for people who are ill  Sick people are permitted to withdraw temporarily from their other roles  Sick people are expected to define their conditions as undesirable and to see and follow competent advice to get better Who gets sick and why  Association between social status and health consistently found across time and place  Theory of fundamental causes  Blends multiple dimensions of SES  Higher SES individuals have access to knowledge, money, power, and social connections throughout life  SES gives people ability to make use of knowledge about how to improve one's health  Education  Education has a direct effect on health, improves self-governing behaviors  Better health behaviors of more educated explains 40% of their health advantage  Income and wealth  More income can purchase more nutritious food, safer environment, and better medical care for children  Family income effect on child health increase over time  Effects are largest for poorest  Race and Gender  Blacks  Have worse health outcomes than whites  Differences more likely to reflect SES differences racial differences  The experience of discrimination and racism can produce stress, which is bad for health  Some evidence from research that people of color receive lower-quality health care  Women  Morbidity paradox  Women live longer (by 5 years) but has more illness  Men more like to engage in risky behaviors  Healthcare spending in the US  Health care spending is a major part of the US economy  The US spends about $2.5 trillion annually, up more than 500% since 1980  US ranks #1 among Organization for Economic Cooperation and Development  US spends $7,960 per person per year, about 2.5 time greater than the OECD country average ($3,233)  If we spent the average, we'd save $1.5 trillion per year  Before the Affordable Care Act, the US Government was already covering about 46% of US Health care costs  Translation: taxpayers were already paying about $3,6660 per person per year  Is US Healthcare "the best"  US ranks 27th in life expectancy and near the bottom third of OECD countries for mortality from disease and injury  Healthcare spending and efficiency  In 2000 the World Health Organization tried to rand the world's best healthcare systems  In their summary the US was 15th in overall performance and 1st in expenditures per capita, giving us an overall ranking of 37  Are really that bad  We are better than average in areas like cancer and acute care in hospitals  We are worse than average in primary care (doctors per capita, initial contacts, consultations) which leads to higher, costly admissions for avoidable diseases Four dimensions of age 1 Social 2 Chronological age 3 Biological 4 Psychological Rethinking Age and Aging  Propose that the current way of conceptualizing age is outdated  Current indicators of old age: proportion of populations 65+, old-age dependency ration, median age  "New" ideas  People have two ages- chronological and prospective (remaining life expectancy)  Instead of "old age dependency ratio" use old age threshold- 15 years  Why should you care about aging  Questions on test  Elderly numbers are rapidly increasing around the world  According to the National Institute on Aging  In 2010, 524 million people were aged 65 or older (about 8%) of the world's population. In 2050, it is expected that 1.5 billion (16%) people will be elderly  According to the Census Bureau:  In 2011, there were 41 (13.3%) age 65 or older, by 2050 it is expected that 81 million (19%) of the nation's population will be elderly  Services to elderly are one of the fastest growing industries  Direct effect on you  The dependency ratio  Size of the non-working age groups (children and elderly) VS the working population 59 (dependents) for every 100 working age Americans  In 2050, it will be 72 to 100  The Sandwich Generation  The first to have significant needs of care for both children and parents in your lifetime Demography  The study of population  Population: why you should care  Economic institutions  What kind of job you will have  The environment  What kind of world will you live in  Geo-political issues  What important resources will be sources of conflict  Quality of life  How nice will it be where you live  Population issues  How many of us are there  7.3 billion people  322 million in US  Where do we live  Distribution  Largest countries and cities  Density (how spread out are we)  90% of the world's population live on 10% of the land 90% live above equator  How does population change  Population Change  What cause population to change  Birth rate (birth/population) * 1000  Fertility = (births/women) * 1000  Death Rate (deaths/population) * 1000  Rate of national increase= births - deaths  Europe isn't growing, US is barely growing  Asia is growing  Migration  Immigrants- emigrants= net migrate rate  Immigration accounts for about 90% of US population growth since 2000  Population Growth through History  World's growth  1 billion- 1804  2 billion- 1927  3 billion- 1960  4 billion- 1974……..  7 billion- 2011  Peak population estimated at 10 billion and will plateau  Bulk of growth has occurred over the past 200 years  Demographic transition  As societies advance, death rates and birth rates decrease  Is there a population problem  Yes- Thomas Robert Mathlus (1798)  Population will grow faster than resources  Population grows geometrically, subsistence arithmetically  The Global Food Crisis: Consumption v. production  No- anti- Malthusians  Science and technology will compensate  No and yes- Marxists  Population Is not the problem, distribution is  16% of world consumes 80% of resources  What does all this mean  Sociology is about understand the human condition, perhaps to improve it, perhaps not. Either way, the endeavor to grasp is at the heart of this science Sociology 100 Final Exam Notes Study Guide  Marriage and Family o Know census definitions of marriage, family, and household. Marriage- Legal union based on mutual rights and obligations Family- Two or more people who are related by blood, marriage or adoption Household- people who occupy the same housing unit Know meaning and examples of rules for mate selection: endogamy, exogamy, hypergamy, homogamy, etc. Exogamy & Endogamy (within group) - Religion and race Homogamy- We tend to marry people who are like us Social status, class Propinquity- social nearness o Know why people tend to follow homogamy rules in marriage. We like people who are like us, and physical attractiveness, social class, etc. o How does interracial/inter-ethnic marriage vary by race and by gender 24% of black males, but only 9% of black females marry non-blacks. 17% Asian males, 36% Asian females. Intermarriage rates for whites and Hispanics do not vary by gender o What do most “mixed marriages” in the U.S. look like ^^ o What are the benefits of marriage Married people are happier, healthier, and better off financially o Know the functions of marriage and family. Reproduction- the "good life" Replacement level/ fertility level- 2.1 Socialization of children Economic security/protection Sexual regulation and the norm of "illegitimacy" o How does conflict theory look at marriage and family. Family transmits inequality across generations Gendered roles reinforced within families o Why are increasing numbers of people (especially women) choosing to remain single Over half of American adults are unmarried (51%), compared to 72% married in 1960. the majority of Americans NO are NOT married Marriage rates have declined o How do men and women vary in terms of how they view cohabitation Men see it as a way to get out of asking a woman to marry her. Instead of popping the question, ask her to move in Women see it as a PRE-MARRIAGE thing. After I move inn, eventually he’ll ask me to marry him o What is “consumer lock in” and how is it related to cohabitation Getting a consumer to consistently use only your product. o What is the divorce rate like for first marriages and for

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Chapter 5.4, Problem 25 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

This full solution covers the following key subjects: . This expansive textbook survival guide covers 34 chapters, and 2741 solutions. The full step-by-step solution to problem: 25 from chapter: 5.4 was answered by , our top Math solution expert on 12/27/17, 07:57PM. Since the solution to 25 from 5.4 chapter was answered, more than 234 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Elementary Linear Algebra: A Matrix Approach, edition: 2. Elementary Linear Algebra: A Matrix Approach was written by and is associated to the ISBN: 9780131871410. The answer to “In Exercises 21- 28, a linear operator Ton n is given. Find, if possible. a basis B for 'R" such thar 25 [T ]” is broken down into a number of easy to follow steps, and 24 words.

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Solved: In Exercises 21- 28, a linear operator Ton n is