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Pro'c that if (u o. uz, .... ud i~ a linearly independent

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

Solution for problem 89 Chapter 1.7

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 89

Pro'c that if (u o. uz, .... ud i~ a linearly independent 'ub>et of n and co. cz ..... ct arc non1ero scalar-;, then (co uo.c2u2 ..... ctu.t} is also linearly mdependent.

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ANTH 1003 Dr. Susan Johnston Class Notes for March 30 – April 1 Human Diaspora (March 30)  Genus Homo moved into the Old World after c. 2 million years ago  Modern humans are the only ones who moved out of the Old World after 200,000 BP  Movement into Asia and Europe was relatively straightforward o Populations expand and move as part of subsistence o Asia and Europe were accessible by land and humans got there by walking (general consensus) o Modern humans did replace already existing hominin populations in those areas  Boats were probably necessary to people the Pacific  Most of North America was likely populated via the land bridge of Beringia that is now the Bering Strait o Boat crossings of Atlantic and Pacific have been suggested as other possibilities, but those are much more significant boat crossings that present other problems that peopling the Pacific does not  Climate and movement o During hominin expansion, it was colder --> water levels of oceans dropped --> more land areas were connected and accessible without crossing bodies of water o The oceans are not necessarily barriers to movement o But sea crossings are deliberate – you must intentionally set out for a distanced island (goal-oriented migration), while land crossings can occur naturally as a result of population expansion or subsistence patterns  Sahul 80,000 – 12,000 BP o More land was available between Southeast Asia and Australian continent which made water crossings less drastic --> land masses were closer o Intervisibility: ability to see another land mass across water from where you are o Evidence for how Australia and Pacific may have been populated o Lake Mungo, Australia (used to be a lake) 40,000 – 30,000 BP  Earliest Australian site that is not disputed  Series of burials, stone tools, fossilized emu eggshells; standard hunter-gatherer site  North America 60,000 – 11,000 BP o Generally colder during Pleistocene, but there were fluctuations o Bering Land Bridge (Beringia) emerged where Bering Strait is today  Wasn’t a “bridge” in the sense we think of it; it was really just land that connected Asia and North America, was populated, not necessarily intentionally used to cross o Sites don’t show up in North America until around 20,000 BP  Ice is destructive to landscape (“scourges” land) o Few early sites on either side of Bering Strait  May be preserved underwater from Beringia, but hard to access  Considerable debate about specific environment of Beringia – very harsh or more mild and inviting – but we don’t really know; would affect whether people migrated “quickly” or not o Native Americans and Asians  Considerable evidence that they are closely related: biological links  Features of teeth that are not functional --> largely genetically determined but not actively worked on by natural selection  “Shovel shape” of incisors, number of roots of molars  Shared by both populations  DNA analysis of a burial from Siberia links that individual to both Eurasian and Native American populations  Diego trait of blood: Native Americans and East Asians are the only groups with relatively high percentages of Diego positive people o The earliest New World sites  Clovis sites show up c. 12,500 BP  More and more new sites are being dated to before that time (20,000 – 15,000 BP)  Meadowcroft, PA (14,000 – 11,000 BP) is a rockshelter with stratigraphic levels pre-Clovis; may date to 17,000 – 16,000 BP or even 20,000 BP at the earliest  Monte Verde, Chile (14,800 BP): incredibly well-preserved remains  Stream action caused site to be waterlogged, which preserved organic material like wooden tent stakes, children’s footprints, chewed tree leaf, worked mastodon tusk, etc.  Paisley Caves, OR (14,270 – 14,000 BP): recovered coprolites with human mitochondria DNA o Basically, people were in North and South America by 15,000 BP and movement into New World likely began around 20,000 – 15,000 BP  Debate #3: other routes into North America o Solutrean tool industry (western Europe, 22,000 – 16,500 BP)  Considerable level of skill required to make the tools  Very specific cultural assemblage  Similarities to Clovis tools suggest a similar technological approach and that one is derived from the other  BUT: stone tools can only be made so many ways and similarities could just be 2 groups solving the same problem in the same way; it is hard to quantify similarity and determine when it is related and when it is not  Also, separation of Solutrean and Clovis tool types in time (3,000 years) is problematic o Lack of site evidence from either end of Beringia: because of the environment, it is reasonable to assume sites around Beringia were not preserved o Argument that people followed seals to North America using pack ice…  Why would they have continued to North America versus going home How would they have known that their destination even existed  Presumably only hunters would have followed seals, not the whole family  Very single-minded interest to have followed seals all the way to North America… especially if seals would have migrated back anyway  Pack ice is not land and is not exactly habitable  May have been a reason for migration of a small group of people, but not likely a scenario for a mass movement of people, and doesn’t really have the evidence that calls for the construction of the scenario  No evidence of catastrophe or significant population shift in Solutrean  Also no evidence that Solutreans even had a reliance on marine animals as a food source o Anzick, MT (12,707 – 12,556 BP): burial of male infant suggests by DNA that makers of Clovis tools are ancestors of Native Americans and that he was related to the Siberian burials, not Solutreans After the Ice Age (April 1)  Pleistocene to Holocene c. 10,000 BP: it gets warmer  Mesolithic (Near East & Europe), AKA Paleoindian (North America) and Archaic o Begins c. 11,000 BP and ends whenever food production starts in the region o Different terminology used for the same time period o Sea levels are rising, land mass disappears or gets cut off from other land mass (coastlines are moving inland) o Changes in land forms; land rises or rebounds once weight of the ice is gone (isostatic uplift) --> also affects relationship between land and water o Changes in resources  Increase in forests/woodland  Appearance of lakes  Species change availability (mammoths go extinct, reindeer move north) and new animals (red deer) are available; their different migration (none or only over a small area) causes different patterns in human movement and distribution  Deer are also smaller and reproduce faster, can tolerate hunting better)  Debate #4: Pleistocene extinctions o Argument that more species/genera went extinct than can be explained by purely climate change  Human arrival in North America coincides with disappearance of these animals and evidence of possible gross overhunting at sites  Historically documented cases of humans moving into an area and hunting a species to extinction (moa of New Zealand, bison of North America)  Sites like Clovis (NM) and Olson Chubbock (CO) show evidence of stampeding and killing larger numbers of animals by several orders of magnitude than they were actually using  Climate change may have been more complex than simple warming and animal species would have had time to adapt  Some modern analogies suggest there may not be much evidence to prove the theory even if it is true and that only 5% increase of predation losses can have a larger effect on animal populations o Arguments against overkill hypothesis:  Chronologies don’t match so well; extinctions occurred both before and after human arrival in North America  If people arrived c. 20,000 BP, why would it take 10,000 years to overwhelm the animal populations  Process of extinctions may have begun before human arrival  The vast majority of extinct species were not hunted in drives (wastefully) like mammoths and bison, or they were not hunted at all  Species went extinct in places where humans were already well-established (Europe) and where humans had not yet established a strong presence  Extinctions in places like New Zealand were the result of new species introduced by humans or environment/habitat destruction  Mesolithic Stone Tools o Most were devised to respond to specific changes in the environment (axes appear in wooded areas) o Some tool types are less frequent (smaller tools for deer hunting increase, larger tools from mammoth hunting decrease) o Star Carr, England (8,700 – 8,400 BCE)  Around a lake  Weird skull that may have been a mask  Fauna includes earliest evidence of domesticated dogs o Vlasac  Return to the same site repeatedly over the years  Cemetery: life expectancy was about 26 years (a lot of kids died)  If an individual survived to adulthood, women lived to 30-39 and men to 50-59  There were 2 women and 8 men over 60 o Clovis and Folsom, New Mexico  Clovis site (13,000 – 12,600 BP) tools included fluted points, supposedly used for hafting to a piece of wood, which appeared all across North America; faunal remains include mammoth  Folsom site (12,800 – 11,700 BP) demonstrated presence of people in North America for a long time  Fluted points in a different style, faunal remains focus on bison o Koster, IL (7,500 BCE – 1,200 CE)  Initially was a seasonally occupied campsite that became a permanent, year- round habitation site The Beginnings of Food Production  Humans happily and successfully hunted and gathered for 95% of human existence  Many cultures continued to hunt and gather after others around them began producing their own food and only stopped when they were forced to (“why plant when the world is full of mongongo nuts”  c. 10,000 BP people in different places independently began to produce their own food and it spread to the rest of the world  Changes in plants: o They get bigger and they can grow in more places o Better for human consumption and more convenient than wild species  Changes in animals: o Tend to be smaller (easier to control) but meatier (more food) o Also less aggressive o Selection for either smaller horns or none at all  The cost of domestication: o Unsheared sheep can hardly walk or see o Corn does not easily propagate itself; seeds are tight to stalk and covered by tight husk  Explanations: why did food production happen o V. Gordon Childe “oasis theory”  It was (incorrectly) thought that it got drier at the end of the Pleistocene so humans and other species congregated around water (oases) --> people observed process of species growing, changing over time, and began to mimic that o Robert Braidwood, Zagros Mountains  People were pushed to the edges of where wild food was most abundant, so they developed agriculture to solve the problem of getting food  Attempt to explain why people altered lifestyle from happily hunting and gathering o Richard Lee, looking specifically at hunter-gatherers  Hunting and gathering in a great way to be in environments of the past; they didn’t work as hard and had more leisure time and better health  So why would they change a lifestyle that worked  Hunter-gatherers are typically mobile with low population density --> need a large area to use but not abuse environment and move to resources  Typically live in small groups and are generally healthy and egalitarian  They have a detailed knowledge of the environment; they would have already observed the process of plant growth  Considerable flexibility in how they exploit the environment  Hunter-gatherer lifestyle is great for abundant environments but can be more stressful in limited environments

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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

The answer to “Pro'c that if (u o. uz, .... ud i~ a linearly independent 'ub>et of n and co. cz ..... ct arc non1ero scalar-;, then (co uo.c2u2 ..... ctu.t} is also linearly mdependent.” is broken down into a number of easy to follow steps, and 32 words. 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. 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: 89 from chapter: 1.7 was answered by , our top Math solution expert on 12/27/17, 07:57PM. Since the solution to 89 from 1.7 chapter was answered, more than 267 students have viewed the full step-by-step answer.

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Pro'c that if (u o. uz, .... ud i~ a linearly independent