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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Question

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?

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