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Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 7 - Problem 7.4.2
Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 7 - Problem 7.4.2

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# find the singular values of the given matrix

ISBN: 9780538735452 298

## Solution for problem 7.4.2 Chapter 7

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 7.4.2

find the singular values of the given matrix.

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Molly Kitchen 2-8-2016 FAD2230 LECTURE NOTES BULDING RELATIONSHIPS (CH. 7) SINGLEHOOD  Never married- doesn't mean that you're not in a serious or committed relationship  Single- could be divorced or widowed  How many stay single o Single and never married are about the same percentage up to the 30's, where the percent of single becomes greater than the percent of never married as age increases  Single typology: o Voluntary temporary- young, college-aged kids who are focused on other things (school) o Voluntary stable- chosen to stay single and is okay with it o Involuntary temporary- someone looking for a relationship but can't find one o Involuntary stable- someone who wanted to form a relationship but has resigned to the fact that it probably won't ever happen, or a widow/ widower who chooses not to remarry after his or her spouse's death FRIENDS This Emotional Life Video  Friendships provide security, support, and a sense of belonging. They also help us solve problems and survive more efficiently.  "You can still be lonely in a crowd," proves that connection past surface connections are important.  Number of friendships between sexes are about the same and are held with the same value, but in general friendships between women are more intimate (more verbal and self-disclosing) whereas with men the relationships are more activity oriented.  In the working class, friendships tend to be longer lasting and more personally intimate than those in the middle class. The working class tends to spend more time interaction to solve problems (work) than the middle class (vacations and independent work because of education).  Hispanic and black youth are likely to have stronger friendships than Asian because the emphasis tends to fall on academics rather than social interactions. CROSS-SEX FRIENDSHPS Molly Kitchen 2-8-2016  They generally develop at school or work where the interaction between same sex individuals may be limited  Discussion: Do you think that men and women can just be friends Why or why not Can a man and a woman have a strict friendship after they have already been in a relationship Why or why not Molly Kitchen 2-15-2016 FAD2230 LECTURE NOTES LOVE AND LOVING RELATIONSHIPS  What is love o commitment o self-sacrifice o affection o patience class def. o optimism o perseverance o deep bond ...toward another person/ between two people o strong affection for one another arising out of kinship or personal ties o attraction based on sexual desire o affection based on admiration, benevolence, or common interests book def. o enduring bond between two people o includes feelings of obligation to another  attachment- a strong emotional bond; safe haven or secure base Video about monkey experiment with wire mother verses cloth mother...goes to cloth mother consistently; "Harlow's Monkeys"  Working Models (way that we perceive ourselves and others)- Adult Attachment Styles o Self  positive- worthy of attention, acceptance and love  negative- unworthy of attention, acceptance, or love o Other  positive- trustworthy, caring, and accessible  negative- untrustworthy, uncaring, and rejecting HISTORY OF LOVE Molly Kitchen 2-15-2016  Classical stories o Odyssey  Early Christianity o love didn't always mean marriage o marriage was practical o sex was for procreation only  18th & 19th centuries o romantic love more prominent o romantic love ideals  love at first sight  only one "true love" per person  love conquers all  the beloved is nearly perfect  should marry for love  19th century Victorian period o men and women in separate spheres o sexual behavior- only vaginal intercourse between man and women  20th century o love and sexuality mandatory o sexual expression basis of marriage  Contemporary love o romantic love: characterized by passion, melodrama, and excitement o Other cultures may think of romance as silly and unnecessary o Our culture views it as utmost importance (when it's not there then the relationship is lost) o Not that important...or is it  Companionate love: type of love that grows over time and is based on strong commitment, friendship, and trust Molly Kitchen 2/10/2016 FAD2230- LECTURE NOTES REVIEW  Singlehood  Never-Married vs. Single  How many people stay single (4%)  Single Typology (voluntary/ involuntary temporary/stable)  Friendships can be beneficial  Race and ethnicity in social relationships  Cross-Sex relationship possibilities  Micro vs. Macro level factors affecting relationships DATING  Dating: mechanism of finding a lifelong mate in order to have companionship, to get married, to share similar interests and beliefs, fun and recreation, social status, intimacy (sexual or emotional), etc.  Early American dating relationships: o Calling- spending time with the family for a couple days in order to get to know the young woman and her family o Necessity of marriage  Industrialization, urbanization, and emergence of dating o Dating roles changed from what we knew in earlier America to these stigmas about guys asking the girls, paying for the date, driving, opening doors, and the girls are supposed to look pretty, maybe prepare the details for the date, etc. o The roles may be changing because women have jobs, so it is more acceptable for the women to help pay sometimes whereas then it was really taboo for the woman to pay. o Principle of Least Interest: unequal emotional involvement between romantic partners that has implications for the quality and stability of relationships  The person with the least emotional involvement has more power in the relationship  The less interested the person is the less fear they have of being rejected  Dating scripts: a set of expectations around dating that differ somewhat for men and women o Women- go to the bathroom in pairs (for some reason), have to look a certain way o Men- ask, plan, pay  How do you know when someone is in a committed relationship o Facebook status o Time people spend together o Holding hands o Wedding ring/ engagement ring...Why don't guys have engagement rings Roles of the man providing- asking- through the ring Molly Kitchen 2/10/2016  Dating trends o Teenagers don't really go on dates- just "hanging out" with a group of friends that creates less pairing off  Homogamous relationships- in relationships with people who are similar to us (age, race, religion, social class, etc.) o Propinquity- living close to someone increases your chances of being in a relationship with them o Pool of eligible individuals- the amount of girls/ guys who are available to you within your location  Where do we meet 2-19-16 FAD2230 LECTURE NOTES Micro-level: Sternberg’s Theory of Love - sees love as having three elements: intimacy, passion, and commitment - Love types o Nonlove o Empty love o Liking o Infatuated love o Companionate love o Fatuous love o Romantic love o Consummate love - A categorization of six types of love that describe how couples are attracted to one another o Eros: passionate, strong physical attraction o Storge: companionate, mutual love Macro-level Perspectives on love - All societies control the development of love to some degree o Arranged marriage example video  What are the benefits  What are drawbacks  Can arranged marriages work How we experience love - Sex, Gender and love o Men report falling in love sooner and with more people than women. o Men are more preoccupied with love than women. - Same-sex love o Primary difference from cross-sex love is the prejudice and discrimination experienced. - Unrequited love o When one person’s feelings are not reciprocated by the other person in the relationship. Breaking up is hard to do - Some stats o 50% of people have broken up with a partner at least twice o 25% have been dumped 6-10 times o Among most distressing events: severe emotional distress - Principle of least interest 2-19-16 - What leads to breakups o Micro-level  Stop communicating effectively  Different interests or values  Personality clashes o Macro-level  Socioeconomic issues impacting income Adolescents in Romantic Relationships - More likely to become depressed - More likely to have alcohol and delinquency problems - Tend to do poorly in school and with parental relationships - Romantic relationships require emotional effort, which can take away from other relationships. Molly Kitchen 2-12-2016 FAD2230- LECTURE NOTES HETEROSEXUAL COHABITATION  Cohabitation- an arrangement of two people who are living together without being married  Who o All groups o About 44% before marriage o From 2000 until now, the number has doubled  Why o Convenience o Financial o Assess compatibility for marriage o Avoid marriage expectations (long term commitment) o Extension of dating o Marriage alternative  In a survey, overall, 46% of all groups think that cohabitation isn't really a huge difference between marriage.  Cohabitation effect- association between premarital cohabitation and pooper marital outcomes o Pooper marital communication in general o lower marital satisfaction o higher domestic violence risk o greater probability for divorce (people who are willing to cohabitate are more willing to end a marriage as well)  Children in cohabitation o 40% have kids (married and cohabiters) o Effect depends on alternatives (i.e. single mom, mom and partner, step- parents, etc.) o Child outcomes: parents who are married have kids who perform better in academics, psychotically, socially, behaviorally, and father involvement relationship  Commitment Theory o Dedication - idea of togetherness and shared meaning; loyal, long- term commitment o Constraint- pressures to remain in the relationship even if they don't want to; financial constraints; children o Sliding vs. Deciding- slowly start to live together = sliding (sleep over, leave things, etc.) vs. sitting down and having a talk about what exactly is happening = deciding  People who decide instead of slide have much less problems than those who slide (kind of mimics marriage as a whole vs. cohabitating as a whole) GAY AND LESBIAN RELATIONSHIPS  APA (American Psychological Association) determined that most gays and lesbians are in a committed relationship Molly Kitchen 2-12-2016  0.6% of population of households  Gay men have less desire to marry (tends to be the case with heterosexual males as well)  Similar outcomes to heterosexual couples on outcomes 2-22-2016 FAD2230 LECTURE NOTES SEXUAL IDENTITY, BEHAVIOR, AND RELATIONSHIPS- OVERVIEW OF HISTORICAL AND CULTURAL INFLUENCES ON SEXUALITY  Mangaia of Polynesian  Dani of Papa New Guinea  Early American views of sex o women- no sexual desire, or else they were considered evil o men- thought to lose natural vitality if too frequent  Industrialization and urbanization o mixing of sexes, freedom, and privacy o sexual gratification became a right o increased birth control methods  21st century o most adults would approve of non-marital sex o majority of Americans believe that it is morally acceptable to have children outside of marriage o longer duration of singlehood increases chances for non-marital sex  consider for a moment...what does this say about our nation as a whole  Sex and gender o sex- biological differences and roles in reproduction o intersex- those born with genitalia that do not clearly identify them as unambiguously male or female  Between 1 and 2 in 1000 people (0.001-0.002%) o Gender- culturally and socially constructed differences between the meanings, beliefs, and practices associated with femininity and masculinity o transgender- feeling comfortable, if not more so, expressing gendered traits associated with the other sex o transsexual- someone undergoes sex reassignment surgery or hormone treatments  0.0001% (males) 0.000033% (females)  sexual orientation- pattern of romantic and sexual partners of choice o heterosexual- having an attraction and preference for developing romantic and sexual relations with someone for the opposite sex o homosexual- same sex o bisexual- both sexes o LGBT Population= 3.4% of adults  What determines sexual orientation o many differing viewpoints o genes, environment o nobody knows for sure  Attitudes toward LGBT community- people believed differently up until about 2008, and now we are separated by opinion again o homosexuality is more socially acceptable o homophobia- having strong negative feelings toward homosexuality What are your views on homosexuality (survey) 1= strongly agree ---> 5= strongly disagree 2-22-2016 1. I worry that gay people will try to seduce me 2. Gay people are immoral 3. Homosexuality is acceptable to me 4. I would not be good friends with someone is I knew he or she was gay 5. I think gay people should not be teachers 6. I usually laugh at gay jokes 7. Marriage between gays is unacceptable 8. I make jokes about gay people 9. Gay people demand too many rights 10. Organizations that promote gay rights are important and necessary 11. I have made fun of a gay person to their face 12. I have damaged the property of a gay person 13. I would feel uncomfortable having a gay roommate 14. Homosexual behavior should be against the law 15. It would bother me to see gays kissing 16. I have never met anyone who is gay What micro and macro level factors have shaped your views 2-26-2016 FAD2230 LECTURE NOTES SEXUAL EXPRESSION THROUGHOUT OUR LIVES (CONT.)  sex and the elderly- people still have sex when they're old  both the quality and quantity of sex is associated with feelings of love for one's spouse or partner  men are more likely to feel that a poor sex life undermines the entire relationship  women are more likely to feel that a relationship can still be good even is the sex life isn't so great COMMUNICATION, CONFLICT, AND POWER IN OUR RELATIONSHIPS  communication- an interactive process using symbols like words and gestures to send and receive messages o communication is a transaction- both sending and receiving o process that is always changing, is different across social classes and racial groups o communication includes co-construction of meanings o communication uses symbols  Race, ethnicity, and communication o among American's English can sound very different o between and within differences- Idaho vs. Alabama  Social class o working class compared to middle and upper class- syntax and grammar  Listening- process of giving thoughtful attention to what we hear 2-26-2016  Active listening- extremely attentive where the listener has good eye contact and body language, and encourages the other person to continue to keep talking  Poor listening- not focusing or paying attention to what the other person says  Verbal communication- spoken exchange of thoughts, feelings, or other messages o Potential barriers for miscommunication  Bypassing- words have several meanings  lack of precision- using improper syntax; "I threw the horse over the fence some hay," vs. "I threw some hay over the fence to the horse."  over-generalizing- "always/ never;" not actually what happens...exaggeration  static evaluation- people make statements that do not allow for change; "I thought you said you didn't like tomatoes."  polarization- black or white; extremes with no middle ground; "I'm right, you're wrong." o Overcoming barriers for miscommunication  Describe your feelings rather than evaluate the behavior of others; "I" statements  Solve problems rather than try to control others  Be genuine rather than manipulative  Empathize rather than remain detached  Be flexible rather than rigid  Present yourself as an equal rather than superior  Nonverbal communication- communicating, without words, by gestures, expressions, and body language 2-24-2016 FAD2230 LECTURE NOTES GENDER AND SEXUAL SCRIPTS  double standard- idea that men are allowed more permissiveness in sexual behavior than women  Learning Activity o What do you believe or what do you think about the double standard o Do you believe that it is fair o What is your perspective from your own gender  sexual scripts- socially learned ways of responding to sexual situations o Male sexual scripts- p. 176  a man's looks are relatively unimportant but his status is enhanced if he's with a beautiful woman  the man always wants sec and is ready for it  all physical contact leads to sex, which equals intercourse, which leads to orgasm  a man is in charge o Female sexual scripts- p.176-177  females should be attractive, but not too attractive  women shouldn't know too much about sex or be too experienced  women shouldn't talk about sex  good girls don't plan in advance to have sex or initiate it  a man should know how to please a woman  sex should lead to orgasm alone, not other stimulation SEXUAL EXPRESSION THROUGHOUT OUR LIVES  sexual behaviors o oral sex- duh o cunnilingus (women being stimulated) and fellatio (man being stimulated)  how many sexual partners do adults have in their lives o one...12% men and 25% women o 2-4...16% men and 33% women o 5-10...26% men and 29% women o 11-20...18% men and 6% women o 21+...20% men and 4% women  early childhood (2-6) years- develop understanding of gendered behavior  middle childhood (7-11 years)- some experiment with masturbation  adolescence is a period when children sexually mature  what are the trends in teenage sexual activity o about 50% of all teenagers have had sex between grades 9 & 12 o about a third of all teenagers are currently sexually active o a higher percentage of blacks and Hispanics are more likely to have had sex, but there's not a huge difference o in the 90's, there was a much higher rate of teenage pregnancy than in 2011, almost double the rates in 2011...could be because of increased use of birth control and because it is more socially acceptable  non-marital sex and young adults 2-24-2016 o non-marital sex= sex prior to marriage o morality  ages 18-24- 70% believe sometimes or not at all wrong  ages 65+- 40% sometimes or not at all wrong  hooking up- sexual intercourse without commitment or even affection for one another o how often does this occur  West coast study- 40% of students had hooked up  southern study- 52% males and 36% females  stanford and indiana- 75% hook up by senior year o reality- men and women prefer dating over hooking up o casual sex related poor phychoogical well-being  gay and lesbian sexual relationships are pretty much the same as heterosexual stats, just more acceptable of multiple partners Molly Kitchen 2-17-2016 FAD2230 LECTURE NOTES THEORESTICAL PERSPECTIVE ON LOVE  Why is it important to understand the following: o theories of love o love types o how love develops  to know if we are in a healthy relationship  to get another perspective about what a relationship should be like  Sociobiological perspective- evolutionary theory that all humans have an instinctive impulse to pass on genetic material o people we marry  women- older men, higher status to support and protect  men- younger women, most fertile  Biochemical perspectives of love- humans are attracted to certain types of people, at which point the brain releases natural chemicals that give us a rush we experience as sexual attraction  Micro level perspectives  Sternberg's theory of love- sees love as having three elements: intimacy, passion, and commitment Molly Kitchen 2-17-2016  John Lee's styles of love- categorization of six types of love that describe how couples are attracted to one another  Reiss's wheel theory of love- how love develops 3-2-2016 FAD2230 LECTURE NOTES WHAT IS MARRIAGE  Marriage- a legally and socially recognized relationship that includes sexual, economic and social rights and responsibilities for partners  Marriage occurs in all societies  Video about a successful marriage MARRIAGE IN U.S. HISTORY  Colonial America- men and women functioned as one because the man had all the rights and represented both himself and the women in most/ all situations  Nineteenth Century- women gained rights and the "one-ness" of marriage became less idealized  Industrial Revolution- caused a middle stage of schooling and relationships within this stage that shifted the reasons of marriage from practicality to love  Sexual Revolution- even before the 60-70's era, there was pre-marital sex  Changing life course patterns- increase in education and college attendance  What is most important in marriage o Love- 88% o Making a lifelong commitment- 76% o Companionship- 71% o Having kids- 49% o Financial Stability- 27%  What is happening to marriage today (2 perspectives) o Marital decline perspective- the view that the institution of marriage is increasingly being threatened by hedonistic pursuits of personal happiness at the expense of long-term commitment  increased divorce rates  increased cohabitation  increased childbearing outside of marriage o Marital resilience perspective- overall marriage is no weaker than in the past, but that all families need an increase in structural support over time  marriage has always had problems (violence or desertion)  marry more intelligently now  real threats- social problems (poverty, discrimination, poor schools, lack of social services)  family issues result from social problems instead of causing them o What perspective do you prescribe to and why 2-29-2016 FAD2230 LECTURE NOTES SEX DIFFERENCES IN COMMUNICATION  On average, women... o conversation is used to establish and maintain relationships o smile more o wider range of emotions via facial expressions and other non-verbal o maintain more eye contact o more qualifiers ("it sort of seems..." or "I would like to...") o more polite tone o ask more questions o more likely to show interest and concern o more personal details and self-disclosure o prefer side-by-side talk  On average, men... o exchange of information o more direct o more assertive o more authoritative and absolute o dominate in mixed-sex contexts  speak more frequently and longer  speak of topics of interest  interrupt more frequently o occupy more personal space o use hands when speaking o more likely to touch others  Why do men and women communicate differently o biological origins- hormones o social origins o nature and nurture..both  Self-disclosure- telling a person something private about yourself that he or she would not otherwise know o Ranges in significance o Unity in Relationships...potential to build or corrode o When it's beneficial, there is reciprocity and disclosure is supported, building trust  Conflict- disagreements over decision making, problem solving, or achieving goals, that can result from differences between group members in personality, perception, information, tolerance for risk, and power or influence 2-29-2016  Styles of conflict o avoidance o accommodate o competing o compromising o collaborating  John Gottman's Four Horseman of the Apocalypse  contempt- feeling superior to your spouse/partner, such as rolling your eyes while the other is talking  defensiveness- self-protection used when one perceives he/she is being attacked  criticism- attacking the partner's personality or character (ad hominem- attack of the person instead of the issue at hand)  stonewalling- withdrawing from the interaction (physically or physchologically) 2-29-2016  belligerence- challenging the authority and power of the other person; testing them 3-14-2016 FAD2230 LECTURE NOTES  Marital decline verses marital resilience perspective (last notes)  Currently (2013) o about 50% men married and about 50% women married o 3% men widowed, 9% women widowed o whites are generally married more than blacks and Hispanics o the rates are declining across races from 1995 to 2013  Why are marriages being delayed o career focus o women aren't as reliant on marriage to have a comfortable life since they can support themselves individually o longer life span because of increased quality of life could possibly delay marriage o increased cohabitation decreases need for marriage o cultural shifts in values associated with marriage and singlehood o occupational and educational opportunities with marriage and singlehood o structural changes in the economy  Qualities for marriage: o honesty o communication o financial stability o responsibility o understanding o quality and stability of parental relationships (how you were raised) o frequent sex o shared values and goals (kids, career, traveling, etc.)  Changing attitudes and beliefs o attitudes about non-marital sex o attitudes about cohabitation o attitudes about non-marital childrearing o attitudes about shared breadwinning o attitudes about division of labor in the household 3-16-2016 FAD2230 LECTURE NOTES- THINKING ABOUT PARENTHOOD  Fertility rate- a measure that is... o average number of children born to a woman during her lifetime o number of children born per 1000 women ages 15-44/49 o number children born per 1000 population  1920's- high fertility rate  1930's- low fertility rate o Great Depression o fewer people marrying o marrying later o families splitting up for employment  1940's-1960's- Baby Boom o greater affluence o marrying younger o less working women (motherhood as the primary cultural goal)  Why does the rate drop in the 60's  less women of childbearing age  changing attitudes of women's social and family roles  more women in college  married women in workplace  How do fertility rates compare among various racial/ethnic groups  Costs and Rewards of Raising Children o Negative- emotional and financial costs  direct financial costs 3-16-2016  lost opportunity costs  stress, worry, disappointment o Estimated $301,907 to raise a child from 0 to 18 years old o Positive- emotional  parents rate what is most fulfilling in life:  85%- relationship with children  24%- jobs/ careers  joy, purpose, fulfillment, satisfaction  Remaining childfree o infertility- inability to have become pregnant after trying for a year o 12% of adults- 7 million people o medical treatment  Assisted Reproductive Treatment (ART)- all fertility treatments in which the egg or sperm (or both) are handled  In Vitro Fertilization (IVF)- eggs removed surgically, fertilized in a dish, then implanted in women's uterus- need 3-4 attempts for success; about$12,000 per attempt  Surrogacy- giving birth to a child for another person or couple  Ethical considerations- lifestyle of surrogate, renting bodies, etc. o Hidden emotions- personal experience, suffer loss on many fronts o Voluntary choice  Adoption o 135,000 children adopted yearly o 1850's Orphan Trains  1850-1929: approximately 250,000 relocated  beginning of organized foster care in U.S.

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