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In Exercises 5–8, find the minimal | Ch 8.5 - 8E

Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay ISBN: 9780321385178 62

Solution for problem 8E Chapter 8.5

Linear Algebra and Its Applications | 4th Edition

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Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay

Linear Algebra and Its Applications | 4th Edition

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Problem 8E

In Exercises 5–8, find the minimal representation of the polytope defined by the inequalities

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Names of researchers: Lainee Foster Language(s): English Dialect(s): (Standard) American English Variable: adjectival form of “drink” Variants: drunk, drunken References: Adamson, S., & Thorne, J. (1990). Papers From the 5th International Conference on English Historical Linguistics, Cambridge, 6­9 April 1987 : Dedicated to the Memory of James Peter Thorne (1933­1988). Amsterdam: J. Benjamins Pub. Co. Vandelanotte, L. (2002). Prenominal Adjectives in English: Structures and Ordering. Folia Linguistica, 36(3/4), 219­259. Wilson, K. G. (1993). The Columbia Guide to Standard American English. Columbia University Press. Chicago Literature Review: At the moment, I have not been able to find many articles that refer specifically to the difference in usage between “drunk” and “drunken.” I have begun instead to look for literature on the general placement of adjectives, prosodic effects on adjective placement/morphology, and adjectival inflection through time. In the Columbia Guide to Standard American English, there is a brief section on the adjectives “drunk” and “drunken”, which mentions that “in all but one situation, drunk appears only as a predicate adjective.” (Wilson, p. 159) The one case in which it appears as an attributive adjective is in the phrase “drunk driving”. However, this phrase is clearly a change from the initial phrase “drunken driving”, a change which was probably caused by headline writers and campaign slogans in a search for shorter phraseology. (Wilson, p. 159) The fact that this phrase has changed, coupled with the fact that this book was published in 1993 (i.e. the research therein was done before that date), I would like to investigate further as to whether there are any other phrases that have undergone this change, or if there is a change in progress as it pertains to the use of “drunk” in place of “drunken.” I am also interested in any phonetic constraints that surround the use of the adjectival forms. If such constraints exist, to what extent do they affect the choice of the variant, and are they categorical, and have they changed at all through time I have found very little literature on prosody in relation to adjectival morphology, but I am still searching for more articles and references that may talk about prosodic influence. Linguistic constraints (if known): Position (attributive/predicative) Productivity Semantic domain of following noun Phonological constraints Social constraints (if known): Historical versus contemporary usage Spoken versus written language Data source(s): COCA and COHA Research question:  Is the adjectival form “drunken” used and if so, in what contexts o Is it in free variation with adjectival form “drunk” Or complementary distribution  When (if ever) did the adjectival form change from “drunken” to “drunk” o Has the distribution changed over time Why Anticipated statistical analysis:  COCA has 450 million words from 1990­2012  COHA has 400 million words from 1810­2009  Data are taken from spoken (transcripts) and written contexts  Corpora will be searched for usage of “drunk” and “drunken” in adjectival contexts o Context surroundings will be examined (i.e. phonology of surrounding words, semantic domain, position, etc.) o Number of tokens and their contexts will be compared to look at change through time Definitions: taken from the Oxford Dictionaries online drunk: adj. Affected by alcohol to the extent of losing control of one’s faculties or behavior: ‘he was so drunk he lurched from wall to wall’ [predicative (drunk with)] Overcome with (a strong emotion): ‘the crowd was high on euphoria and drunk with patriotism’ [attributive] drunken: adj. Drunk or intoxicated: ‘gangs of drunken youths roamed the streets’ Preliminary results from searching the corpora: COCA:  Drunk: o 456 occurrences  Spoken occurrences: 144  Written occurrences: 312  Academic occurrences: 41  Fiction: 95  Magazine: 86  Newspaper: 90  “Drunk with” [predicative]: 170 occurrences  Drunken: o 307 occurrences  Spoken occurrences: 18  Written occurrences: 289  Academic occurrences: 23  Fiction: 67  Magazine: 37  Newspaper: 162  “Drunken with” [predicative]: 0 occurrences COHA:  Drunk: o 182 occurrences  Spoken occurrences: No info available  Written occurrences: Appears to be all  Looking at the spread of occurrences throughout the years (1810­ 2000, 10 year intervals), it looks like the usage of “drunk” is greatest in the 1970s and in the 2000s, but not as pronounced in the 1980s or 1990s  “Drunk with” [predicative]: 512 occurrences  Drunken: o 225 occurrences  Spoken occurrences: No info available  Written occurrences: Appears to be all  Looking at the spread of occurrences throughout the years (1810­ 2000, 10­year intervals), it looks like the usage of “drunken” is greatest between the 1960s and 1980s  “Drunken with” [predicative]: 48 occurrences Preliminary Conclusions: From the first look at the COCA corpus data, it would appear that “drunk” is the current favored adjectival form, but in the past, judged by the COHA corpus, there were more occurrences of “drunken” than “drunk.” Interestingly, the intervals during which each variant was used overlapped somewhat. Also, it would appear that historically, “drunken” was also used as a predicative adjective, a trait that seems to have disappeared in its more modern usage.

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Chapter 8.5, Problem 8E is Solved
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Textbook: Linear Algebra and Its Applications
Edition: 4
Author: David C. Lay
ISBN: 9780321385178

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In Exercises 5–8, find the minimal | Ch 8.5 - 8E