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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, and Bleyer. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors: [26] 5 5 61 -8-8 11 b = 13 63 11 14 Vigoro V = T(x) = P = Parker Bleyer 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. X

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, and Bleyer. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors: [26] 5 5 61 -8-8 11 b = 13 63 11 14 Vigoro V = T(x) = P = Parker Bleyer 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. X

Advanced Engineering Mathematics
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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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, and Bleyer. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors: [26] 5 5 61 11 b = 13 63 11 14 Vigoro V = T(x) = p = Parker 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. B Bleyer X
Transcribed Image Text: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, and Bleyer. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors: [26] 5 5 61 11 b = 13 63 11 14 Vigoro V = T(x) = p = Parker 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. B Bleyer X
Then find a formula for T-¹, and use it to determine the amount of Vigoro, Parker, and Bleyer required to produce 268 pounds of nitrogen, 634 pounds of phosphoric acid and 657 pounds of potash. T-¹(y) T [268] 634 657 B y
Transcribed Image Text:Then find a formula for T-¹, and use it to determine the amount of Vigoro, Parker, and Bleyer required to produce 268 pounds of nitrogen, 634 pounds of phosphoric acid and 657 pounds of potash. T-¹(y) T [268] 634 657 B y
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