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Prove that the triangle inequality is an equality if and

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

Solution for problem 89 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 89

Prove that the triangle inequality is an equality if and only if u is a nonnegative multiple of v or v is a nonnegative multiple of u.

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Geo 101 – The Dynamic Earth Exam 4 Study Guide THIS IS NOT ALL INCLUSIVE – especially if you don’t fill it out fully.  What are the types of fossilization that we covered and how do they work o Frozen or Dried o Amber or Tar  Sticky sap on a tree, tar is when oil has seeped to the surface looking like a drinking hole o Preserved or replaced o Permineralization o Carbonization o Molds and Casts (Replica or original) o Trace Fossils o Extraordinary fossils (DNA)  What are evolution and natural selection o Evolution  Both fact and theory  Change in a population over a succession of generations, due to the transfer of inheritable characteristics o Natural Selection  Is theory that explains fact  Organisms are different  Same differences are advantages  More advantages = more offspring  Population of organisms are always changing to adapt to their environment  What are some the many pieces of evidence that help us understand how organisms evolve o Anatomy­ skeletons, teeth, anything left behind  Fossils  Modern o Vestigial organ  Organ that no longer functions in the same way that it did o Embryology  Way bone develops o Genetics  PNAS  Phylogenic relationships among the major cetartiodactly subgroups o Biogeography o Homology  The sameness  How anatomy looks the same in different creatures  What causes extinction o Climate change o Tectonic activity  Causes sea level to rise  Habitat changes o Asteroid or comet impact o New Predators  You must know the definitions of the relative dating techniques we covered in class and be able to use them like we did during the class activity. o Original Horizontality  How sediment is deposited  Fairly horizontal o Superposition  Applies to  Sedimentary only  Undeformed  Older on bottom  Can get tricky o Lateral Continuity  Sediments are deposited in continuous layers  Can be distributed later o Cross cutting relationships  Formations in relation to each other  Baked contact  Inclusions  What do unconformities tell us o Abrupt transitions in a stratigraphic column  Missing time  Non deposition  Erosion  How do geologists use fossils for dating o Principle of Fossil Succession  Fossils are found in limited strata  Found in a definable order (amphibians, mammals, etc.)  Don’t reappear o How we use fossil  Index fossils Trilobites  Well dated  Widespread  Short lived  How was the geologic column created o Represents entire Earths History o Graphic representation of the layers of rock that make up the earths crust o Divided into segments each of which represents a specific time interval  How does a radioactive isotope give us a numerical age o Decay and Half Life  Unstable atoms eject particles predictably  Become more stable atom (14C – 14 N)  Parent isotope  Daughter Isotope o Half Life  Time it takes for half of the population to decay  Cannot predict when single atom will decay  What characteristics does an object need in order to be dated with radio­isotopes o Carbon dating  What can be dated with radioactive methods  What other methods can you use to determine a numerical age o Igeneous rocks o Metamorphic  Sometimes, depends on temperature and mineral type  What did we date to determine the age of the earth o 4.5 Billion Years old  Know the major events in each eon or era that we covered in class: names of supercontinents, big geological events, types of life that first appeared. (Use the handouts – they will make studying so much easier!!) Hadean Eon ­ 4.55 Ga formation of Earth ­ 4.5 Ga differentiation o Dense materials sink ­ 4.5 Ga formation of moon ­ Before 4.4 Ga o Molten tock surface o Non oxygen atmosphere o No water ­ After 4.4 Ga (Australian zircon) o Maybe solid rock o Non oxygen atmosphere o Some water ­ 4 Ga Meteor o Destroyed existing surface o Surface reformed  small volcanic islands ­ End of Hadean Eon o No life o Very little land o Acidic ocean not made out of water Archean ­ Paleogeography o 80% of continental area ­ Seas and Atmosphere o Liquid water to create seas o Not much oxygen in atmosphere ­ First Life o Earliest fossil  3.5 Ga  Single cell  Carbon isotopes  Stromatolites  Algae mats  Photosynthesis (creates oxygen)  2.95 Ga  Helped increase oxygen Proterozoic Eon Start Paleography ­ 90% of continental crust that we have today ­ This is growing throughout the entire eon Supercontinents ­ Large land masses­ nearly all continents ­ Constant splitting and reassembling ­ Profound affect on climate Rodinia – first supercontinent Pannotia­ reverse of rodinia Atmosphere ­ Amount of oxygen increases so much ­ Algae is causing the leap of oxygen ­ How do we know this o BIF­ bandit iron formation  Cannot form unless a certain amount of oxygen is in the air o This changes chemistry of ocean Life ­ Eukaryotic evidence = 2.7 Ga ­ First fossils from 2.1 Ga ­ Symbiotic relationship Life Plants ­ Ocean – algae ­ Land­ algae o Fungi fossil­ 650 to 544 Ma o Molecular clock= 1.3 Ga Ediacaran Fauna – soft bodied – very unlikely we have the fossils for them ­ 565 Ma (million years) ­ Worms, jellyfish ­ No shells ­ Underwater Soft bodied fossils Snowball Earth – glaciers everywhere ­ Glaciers on land ­ Possible frozen ocean ­ Mass extinction ends eon End of the Proterozoic o Paleozoic Era  Early o Break Up of Pannotia o Epic Continental seas o Taconic Orogeny o New England o Ends in glaciation  Life o Cambrian Explosion  Massive diversification of life  Plants o Ocean  Algae  Seaweed o Land  Simple Fungi  Algae  Liverwort  Animal o Diverse shelled animals o Triobites o Sponges o Corals o Echinoderms o First Vertebrate  Jawless Fish  Middle  Paleogeography o Climate warmed and sea level rose  Reefs o Progenies  Plants o Vascular plants  Woody tissue, seeds, veins  Could grow larger o Large swampy forests (mosses and ferns)  Animals o Diverse shelled animals o Fish: Jawed, lobe fin, ray fin o Spiders and insects o 1 amphibians  Tiktaalik o Cross between fish and tetrapod o Fish  Fins  Scales  Gills o Tetrapod­ anything that has these four appendages  Flat head  Ribs  Neck  Fins support weight  Late  Paleogeography o Global cooling  Sea level drop o Pangaea forms o Alleghanian Orogeny  Appalachians  Ancestral Rockies  Plants o Gymnosperms  Conifer  Cycads (palm like)  Ginkgo  Animals o Amphibians Diversify st o 1 reptiles  eggs with shells  End  Giant extinction event at 248 million o 96% of marine species o 70% of terrestrial species o largest in history Mesozoic Early Paleography  Break up of Pangaea  North Atlantic Ocean  Inland seas Plants  Gymnosperms diversify Animals  1 swimming and flying reptiles  1 turtles  Coral Dinosaurs!  Warm­blooded  Huge sauropods  Feathered birds­ last dinosaurs Mammals  Very small  Not like modern Late Paleography  Pangaea broken o India  Warming and sea level rise o Inland seas  Laramide orogeny Plants  1 flowering plants  Flowering plants and hardwoods take over Animals  Modern fish  Dinosaurs diversify  Mammals diversify End of Mesozoic  K­T boundary extinction event o Meteor o Dinosaurs (except birds) o 75% plant life Cenozoic Paleogeography  Himalaya formation  Atlantic and Pacific separated Climate  Cooler climate o Grasslands  Ice age: o Creates land bridge Plants  Flowering plants and gymnosperms diversify st  1 grasses Animals  Mammals diversify and flourished o Giant mammals at first  What is the extremely general history of human evolution (What did the graph on the slide look like)  How do the various fossil fuels form o Sun  Solar energy  Plant Matter  Fossil Fuel  Wind o Gravity  Tides  Falling Water o Chemical Reactions o Nuclear Fission o Geothermal – happens in the center of the Earth o Oil and Natural Gas  Hydrocarbon compounds  Remains of marine algae and plankton  In what geological formations do different fossil fuels get trapped o Anticline o Fault o Salt Dome o Stratigraphic  What methods do we use to extract fossil fuels o Tar Sands  Viscious oil in sand  Cannot Pump  Mined then heated  Heated then pumped  Very expensive o Oil Shale  Has not reached oil window  Mined then heated  Very expensive o Fracking  Hydraulic Fracturing  Extracting natural gas  Increases well production  Drawbacks  Groundwater contamination  Land use issues o Extracting Oil and Natural Gas  Drilling  Puncture the seal rock  Pumping  Brings oil to the surface o Refining Oil  Crude oil is distilled  Process depends on grade  Sulfur content  Specific gravity  Are we running out of oil What are the various answers to this question o Other sources exist  Liquidfied coal  Oil shade  Tar Sands  Methane hydrate o Not economically viable at current prices and technology o Will we run out  Geologists  Soon  Economists  Will stop using it first  What are the drawbacks of fossil fuel use o Air Pollutions  Particles and gases  Acid Rain o Carbon Dioxide  Greenhouse gas o Byproducts  Mine runoff o Spills  Groundwater  Ocean o Fatalities in mines  A lot  What are the types of alternative energy we covered What are their advantages and drawbacks o Nuclear Power  Energy release when nucleus is split (fission)  Drawback  Controlling nuclear reactions o Lot of work and planning o Potential meltdown  Nuclear waste  Damaging to living organisms  Long time decay (decades­ centuries) o Wind  Must have steady breeze  Clean  Drawback  Noisy  Ugly  Hazard to Wildlife o Solar  Sunlight converted to electricity  Clean  Drawbacks  Not efficient  Not cost effective o Hydroelectric  Two Kinds  River o No pollutants o Drawbacks  Damns  Tidal o No pollutants o Drawbacks  Construction o Geothermal  Use the earths eternal heat where it come near the surface  Used in two ways  Water  Steam to turn turbines  Drawbacks  Conditions limited Extra office hours for exam prep: Monday, April 11 from 12:00­2:00pm (if these don’t work, email for an appointment)

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Chapter 6.1, Problem 89 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. Since the solution to 89 from 6.1 chapter was answered, more than 234 students have viewed the full step-by-step answer. The answer to “Prove that the triangle inequality is an equality if and only if u is a nonnegative multiple of v or v is a nonnegative multiple of u.” is broken down into a number of easy to follow steps, and 27 words. The full step-by-step solution to problem: 89 from chapter: 6.1 was answered by , our top Math solution expert on 12/27/17, 07:57PM. Elementary Linear Algebra: A Matrix Approach was written by and is associated to the ISBN: 9780131871410. This textbook survival guide was created for the textbook: Elementary Linear Algebra: A Matrix Approach, edition: 2.

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Prove that the triangle inequality is an equality if and