Problem 2 Find a linearly independent set of vectors that has the same span as1-----| 42 = 2-2=-111If yea, finCom4=and us1201and us =H1-1-11

Answered: Image /qna-images/answer/61f9330c-8888-42e8-9033-7231a195dba3.jpg

Answered: Problem 2 Find a linearly independent…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Consider the collection of vectors --0-0-0) Is S linearly independent or linearly dependent? If S is linearly dependent, write one vector as a linear combination of the others. Show all of your work S = 5
Suppose that you are in the garden supply business. Naturally, one of the things that you sell is fertilizer. You have three brands available: Vigoro, Parker's, and Bleyer's. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors T(x) = 2 ---A 32 p= b= = 11 Parker's Bleyer's T-¹(y) = V= T-1 7 66 Vigoro Determine the linear transformation T: R³ R³ that takes a vector of brand amounts (in hundreds of pounds) as input and gives the nutrient vector as output. Then find a formula for T-1, and use it to determine the amount of Vigoro, Parker's, and Bleyer's required to produce 44 pounds of nitrogen, 200 pounds of phosphoric acid and 412 pounds of potash. 44 (1)- 412 X 11 2 23 y
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12 If a. x and y are three non-zero and mutually non-parallel vectors, and the vectors b and e are given by b=x-(x-â)â and c=y-(y â)â-(y.b)b, where â and b are unit vectors along a and b respectively, show that a, b and c are mutually perpendicular.
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Problem 2 Find a linearly independent set of vectors that has the same span as U1 = 1 1 -1 1 , U2 = 1 2 , uz = 1 -1 , U4 = 1 2 and us =