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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 2.6 - Problem 8e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 2.6 - Problem 8e

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# Solved: Let C be an n × n consumption matrix whose column ISBN: 9780321982384 49

## Solution for problem 8E Chapter 2.6

Linear Algebra and Its Applications | 5th Edition

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Problem 8E

Let C be an n × n consumption matrix whose column sums are less than 1. Let x be the production vector that satisfies a final demand d, and let ?x be a production vector that satisfies a different final demand ?d.a. Show that if the final demand changes from d to d + ?d, then the new production level must be x + ?x. Thus ?x gives the amounts by which production must change in order to accommodate the change ?d in demand.b. Let ?d be the vector in Rn with 1 as the first entry and 0’s elsewhere. Explain why the corresponding production ?x is the first column of (I – C)–1. This shows that the first column of (I – C)–1 gives the amounts the various sectors must produce to satisfy an increase of 1 unit in the final demand for output from sector 1.

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##### ISBN: 9780321982384

This full solution covers the following key subjects: production, demand, let, final, column. This expansive textbook survival guide covers 65 chapters, and 1898 solutions. Since the solution to 8E from 2.6 chapter was answered, more than 272 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 8E from chapter: 2.6 was answered by , our top Math solution expert on 07/20/17, 03:54AM. Linear Algebra and Its Applications was written by and is associated to the ISBN: 9780321982384. This textbook survival guide was created for the textbook: Linear Algebra and Its Applications , edition: 5. The answer to “Let C be an n × n consumption matrix whose column sums are less than 1. Let x be the production vector that satisfies a final demand d, and let ?x be a production vector that satisfies a different final demand ?d.a. Show that if the final demand changes from d to d + ?d, then the new production level must be x + ?x. Thus ?x gives the amounts by which production must change in order to accommodate the change ?d in demand.b. Let ?d be the vector in Rn with 1 as the first entry and 0’s elsewhere. Explain why the corresponding production ?x is the first column of (I – C)–1. This shows that the first column of (I – C)–1 gives the amounts the various sectors must produce to satisfy an increase of 1 unit in the final demand for output from sector 1.” is broken down into a number of easy to follow steps, and 148 words.

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