7. (a) Use a matrix method to find the relationship between the constants a and b for which the system of equations u+2v +3w = a, u-v+w = 1, 2u + v+ 4w =b %3D has solutions. When a and b satisfy this relationship, find all of the solutions to this system in terms of a and write your answer in vector form. (b) In a market, the price of a share t seconds after the market opens is p(t) dollars. An analyst constructs a model which predicts that the price of this share should vary continuously with time according to the differential equation dp = p(t) - e. dt %3D If the initial price is $1, solve this differential equation to find p(t). Show that, according to the model, p(t) is increasing for all t > 0. When will the price of a share reach $1.25?
7. (a) Use a matrix method to find the relationship between the constants a and b for which the system of equations u+2v +3w = a, u-v+w = 1, 2u + v+ 4w =b %3D has solutions. When a and b satisfy this relationship, find all of the solutions to this system in terms of a and write your answer in vector form. (b) In a market, the price of a share t seconds after the market opens is p(t) dollars. An analyst constructs a model which predicts that the price of this share should vary continuously with time according to the differential equation dp = p(t) - e. dt %3D If the initial price is $1, solve this differential equation to find p(t). Show that, according to the model, p(t) is increasing for all t > 0. When will the price of a share reach $1.25?
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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