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For all vectON u. 1', and w in n3' prove that (u x v) x w

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

Solution for problem 117 Chapter 6.1

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 117

For all vectON u. 1', and w in n3' prove that (u x v) x w = ( w. u)v - (w. v)u.

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5) Defining & Parameters of Study of Law 02/03/2016 ▯ Jurisprudential View of Law: Inside the box view.  Law School idealized version where law is a closed system of rules and principles, but this is a mythical status.  Read the law in a statute to find what it is.  Institutions: Courts, practices, law schools, the Bar, etc. Used to transmit these rules and ideas that guide us in society.  Holy Book (religion) = Law Book (legal): Rules to how to live life, Pope Vs. The Court. Parallel between the two. o Canon law, theocracy, Israel. ▯ ▯ - Brown V. BOE: Plessy was precedent (separate but equal) and didn’t want to challenge that decision previously. Can’t apply to education because th not equal protection under the law (14 ) according to Brown. Movie Clip:  “I want justice for him to the full extent of the law” VS. “Law and justice are distant cousins and here in South Africa they’re not on speaking terms at all. o Law and justice are not always the same thing, law as a way to arrive at justice.  Law provides a context in which we struggle over moral issues. ▯ ▯ Law as a game (Sutton):  Rituals, rules, and sets of procedures. Nonviolent way to resolve disagreements. o Rules favor certain actors of the competing groups. o People that use court often are more successful than those who use it less. o Law on the books vs. law in practice. o Is it more important to follow the rule of law or the idea of law in terms of achieving justice. What is law according to the rules (procedure)  Winners have the best knowledge, strategy, etc. Not necessarily the most noble. Kill or be killed to win the case.  Link to legal positivism: Law is what has been posited, ordered, practiced, tolerated. Is (what does the law actually say) rather than ought (what it should say). o Ritual: Process over substance. Structure of government. o What the law means in terms of policy. Is it actually the law. o Follow the rules for the best outcome. The rule of law is the measure of problems and need to respect outcome as correct.  Amoral: Neutral as to the very question if this is ethical or unethical from perspective of morality. Doing it because its what I have to do.  Opposite of cause lawyering. o Process is greater than substance. IS > OUGHT. Sources/Authority > Substance.  The lawyer need to find if the claim has a stake in court. o Democracy: The is and ought can come together. There ought to be gay right for marriage so turned it into an IS in California.  Emphasis on ought is making a new set of enforceable rules to impose as what is. Open to public opinion.  Want set of values to turn into a particular set of rules, brings in factor of legitimacy.  Higher chance of being legitimate if its also legal. Especially in democracy. o What lawyers know and do.  Change rules internally opposed to externally. Used same tool set (law) to dismantle it (broader legal canon). External is civil disobedience, social media, etc.  More legitimate to change it internally, might need to use external to push the internal change. ▯ ▯ Legal Positivism: Idea that we have to have rules and institutions in society in order to achieve law as a certain status. Based on legal institutions rather than based on ideas of justice. Law is what has been ordered or decided by the governing body. ▯ ▯ Law from the view of Sociology:  Legal positivism of law as social construction, law is made by people in institutions. Not really tangible. o Institutions matter a lot, can’t just do what we think is right.  Overlapping ideas about law from and within different disciplines and fields. Sociology of law (theory of how law explains emergence of society, how society explains emergence of law), law in society (interdisciplinary, how law and society affect each other), law as politics and policy, approaches. o Outside the box: law and power, law and social change, etc. o Law is plural not singular. o Legal Consciousness: ▯ ▯ Law and Sociology: Dedicated to studying the legal behavior of human groups.  Law is a group activity: Citizens need to follow the rules and enforcers. Need structure and institutions to facilitate rules.  Behavioral system: Distinct roles, hierarchy, and always be discretion to the institution. o There is always some variation. In practice the rule is applied differently to different groups (Calavita).  Normative Vs. Positivist tensions. ▯ ▯ Law and Sociological Theory:  Explain realities, facts, etc.  Explain society or aspect of it (race, economics, etc.)  Focus on theories of law but there is engagement between legal theories, socio-legal theories, etc. ▯ ▯ Natural Law: What is inherently known as law. Might not always coincide with the actual law.  Connection to quest of justice and morality.  Usually religious but can also be secular (nature, human history). o Religion has different idea of what is natural and also based on religious morality. Who gets to interpret this law (pope canon law)  Universal, timeless, and transcendent moral principles that are the basis of ethics, norms, and laws. o Should be universal, timeless, and transcendent. Skeletaly rooted in morality and truth. True law as being ethical.  Exists independently whether or not it is written or codified by peoples, It doesn’t have to be acknowledged or codified in order to exist.  Declaration of independence, Locke, Jefferson, etc. o What we want or should be there in law as inherent. o Declaration: shows ideals and ideas of natural law.  Power not granted by blood but given by the people (consent and mandate).  All men created equal under god. o Founding was about breaking unethical human law, and stand up for natural law principle. ▯ ▯ Evolutionary Theories:  Progressive change where the fittest survive, analogy to biology.  Teleology: Assumption that there is change towards a particular change. Conscious and unconscious recourse to idea of evolution. o Positive is built upon and negative disappears or dies. o Logical connections in the past, and how it functions to create the present. o In hindsight can see why things turned out the way they did.  Emphasis on the individual, separated from the community. Agency is greater than structure. o People and groups can break from the structure, don’t give enough of what is needed to those in that place and time. ▯ ▯ - Henry Maine: 1800’s England.  Law shaped by a society’s history and associational form.  Three stages of history: o In the beginning the situation of society was given to them. No choice as to what role was in society. Lords and serfs in feudal society. Born to what you are and die as that as well. No choice to shape destiny, law is given by structure and power. No legal equality between and among people due to station being dictated by ascription rather than the law. o Modern Society: Everybody equal under the law. People now have a choice in how they do or don’t interact with each other. Contractual arrangement.  Movement from ascribed statues to individual autonomy and there fore voluntary ability to make contracts. o People are equal in ability to enter and leave contracts. Status is not given to you, aside from equality. From that point you can make contracts that could improve your position. o Could result in cases of inequality due to arranging elevation of the self that others could not.  Modern law recognizes the legal equality of all, without reference to status. Including right and necessity to freely enter into contracts  Methodology, ideology, and impact. o His view is flawed, makes up history. Developing theory based on a world view that he would like to support not necessarily the reality. o Capitalism assumes legal equality and contracts around wage labor. Selling time and skill to employer for a wage.  These people not always able to enter into contract on their terms and don’t have exit strategy. Employer has greater flexibility. o Some governments give more or less protection to some employers and workers.  Strong justification for ideals and ideas for equality of contract in a capitalist marketplace, sometimes reality sometimes not. ▯ ▯ -Emile Durkheim: Values in social formation. Group of people having shared values.  All societies are moral in the sense of having values. o Societies organize in part using values that they can rally behind.  All societies need values as a basis for solidarity o Need to have shared values to have a connection to one another.  Law expresses and transmits values o Law is a glue that functions as moral value. Means of transmitting values in society.  But even violating the law can be useful. Wrongdoing helps community to define societies boundaries and norms. o When rules are violated, adds to social identity and cohesion. Allows to enforce and reaffirm values in the first place.  Modern economic diversity (division of labor)  We need each other  Increases mutuality and shared values  Law o Economics affects cohesion. In history people were more economically independent, would do everything themselves.  Resulted harsh treatment of each other. However this was not true rather the opposite.  More accepting of people making mistakes and more rehabilitative. o Modern day more interdependent, but we are harsher than older societies.  Law is more restitutive than repressive. Need to return to cooperation and restore harmony when law is violated. o Division of labor leading to where we need to value each other, can’t survive without each other.  Values follow material and economic conditions and survival needs.  Need to look at social facts to understand society, legal facts are a sub section of this. o Social Facts: Objects or assumed ideas for how the world works. o Common sense among the people of that society. God will protect you, women and men as equals, etc. ▯ Durkheim & Law:  Law is a product of changing morality driven by the division of labor. o Law represents collective conscious and point of view. o Doesn’t take into account difficulty in arriving at the collective conscious.  Law is a social fact that represents the collect conscience  Law symbolizes social solidarity and connectedness. ▯ Durkheim & Informal Law:  In some communities public opinion is greater than formal rules in terms of controlling behavior. o Will transfer values into law, however this is not always the case. o Can become into non codified laws or recognized, but have effect of law. More like social implication and acceptance. o Strong opinion can drive the changing of rules because values matter so much. Law is expressed in how we act.  Formal law emerges where informal law not strong enough. ▯ Durkheim &Crime:  Conceptual Definition: Emphasis on link between crime and collective conscience. o Collective conscience could be different in different areas. o Unofficial bodies of law makers would them give a different collective conscience. o Organizations that violate law have very strong social codes. May be even more rigid sense of unofficial law.  Gangs, jails, etc.  Operational Definition: Any action that evokes punishment. Observable. o Violations of community values are not always clear but can still be felt.  Can turn into something seen if there is punishment for it, becomes more material. o Helps us determine if we are on the right side of society, good people because not like them. Keeping the rules (values) and laws (ethics and morals) rather than violating them.  Crime allows the arousal and reaffirmation of the collective conscience: o Crime as function and in reinforcing society. o Crime can be innovative and encourage individualism.  Questioning of authority of Socrates is mainstream today.  Legal Marijuana used to reorganize society.  Rate of crime in a given society will tend to be constant over time. Empirically wrong. ▯ Law: Symbol & Sacred:  Sacredness is an attribute of all societies including modern societies. o Secular religion = law. What is sacred may change but the fact of sacredness does not. Superiority of the law so cannot be challenged.  Law is one of the social institutions which we experience as sacred  The important expressive role of law, o Prison as a symbol of political power o Moral right. ▯ ▯ ▯ Maine:  Emphasis on status and contract.  The level of contemporary, written 150 years ago.  Dominance of capitalist and democratic legal based system.  Contract to determine human relations (legal equality). Allows for contract underscoring equality and allowing pursuing of goals.  More focused on the economic aspect ▯ ▯ Status rather than legal equality has applied historically and today  Lack of ability to engage in contract in a way not fitting. o Segregation during the 50’s o Caste system in India: No longer legal but still social. o

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Chapter 6.1, Problem 117 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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For all vectON u. 1', and w in n3' prove that (u x v) x w