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determine whether the given orthogonal set of vectors is orthonormal. If it is not

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 5.1.13 Chapter 5

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 | ISBN: 9780538735452 | Authors: David Poole

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

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Problem 5.1.13

determine whether the given orthogonal set of vectors is orthonormal. If it is not, normalize the vectors to form an orthonormal set.

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iClicker Which two species in the tree below are most distantly related A) 2 & 3 B) 4 & 2 C) 1 & 3 D) 1 & 2 E) 1 & 4 HUMAN EVOLUTION • It happened (& continues)! • Humans aren’t special to not evolve – We’re just like any organism on the planet • We have EVIDENCE – Much science, many books that aren’t just anecdote • Unfortunately, some people just don’t understand or trust this (or other) science – They will just get Left Behind What allowed humans to evolve in the first place • Ultimate reasons: – Chance events – Other extinctions and subsequent adaptive radiation • More Proximal reasons: – Plate tectonics – Adaptation to a rapidly changing environment 3 million years ago >3--10 million years ago The Great Rift Valley The overall accepted picture of homonid fossils over the past 4 million years Some fossils are hard to place and their position is still being debated (based on EVIDENCE) This figure does not include all fossil species ‘Lucy’ Specimen of Australopithecus afarensis ~3.2 million years old discovered in modern Ethiopia Figure 20-1 Early analysis of these relationships left much controversy; hard to discern until further molecular analysis Figure 20-2 “I ain’t evolved from no chimp” Well, you’re right! They’re our evolutionary cousins! Figure 20-3 Four possible evolutionary scenarios after looking at much data; most probable is ‘a’ Figure 20-7 Data that helped resolve this tree (2001—see text) came from dozens of genes and very strict/conservative analysis bars represent standard errors and confidence intervals Each and every independent test and verification has come up with nearly the exact same tree and even more precise results as our technology has gotten better One of the strangest questions some people ask about evolution: • If humans evolved from other primates then why do those primates still exist • Their way of life continues to work • Think about the variation in populations; some individuals used a new resource or outcompeted others in an isolated population and took a new evolutionary trajectory Figure 20-8 New molecular technology allows us to conduct analyses at an even greater level! Human chromosome two is essentially a combination or fusion of two separate chromosomes Deletion of some genes Genes unique to humans Figure 20-9 Figure 20-13 Figure 20-19 Figure 20-20 Neanderthal reconstruction Figure 20-22 Figure 20-23 Figure 20-26 Figure 20-29 Figure 20-31 iClicker Which species has an evolved trait that is most recently diverged and that is unique to that lineage A) 2 B) 3 C) 1 D) 4 E) None Generalized human migration 100,000 ybp—15,000ybp Figure 20-36 Figure 20-37 A few similarities in some primates Figure 20-41 Unnumbered figure page 769 Molecular analyses have solidified some facts about human evolution • We continue to find more evidence • Analyses are getting stronger • Where do we go from here

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Chapter 5, Problem 5.1.13 is Solved
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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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determine whether the given orthogonal set of vectors is orthonormal. If it is not