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Ayanokouji and Sakayanagi are trying to take control of the DCS building! Let A(t) and S(t) be the amount of territory (in square meters) each of them cover at a given time, respectively. These values change dynamically according to the system of differential equations with initial conditions A(0) = S(0) territory. A' = wA+S+ et S' yA+S+t 1. Assume these changes stop once someone runs out of Let (w,x,y,z) (1,-1,-1,1). Who eventually runs out of territory, and at what point in time does this happen? Suppose the second equation was S' = yA+ zS+ e² instead. Let (w, x, y, z) = (0.5, 1, 1, 2). Who eventually runs out of territory, and at what point in time does this happen?

Ayanokouji and Sakayanagi are trying to take control of the DCS building! Let A(t) and S(t) be the amount of territory (in square meters) each of them cover at a given time, respectively. These values change dynamically according to the system of differential equations with initial conditions A(0) = S(0) territory. A' = wA+S+ et S' yA+S+t 1. Assume these changes stop once someone runs out of Let (w,x,y,z) (1,-1,-1,1). Who eventually runs out of territory, and at what point in time does this happen? Suppose the second equation was S' = yA+ zS+ e² instead. Let (w, x, y, z) = (0.5, 1, 1, 2). Who eventually runs out of territory, and at what point in time does this happen?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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Ayanokouji and Sakayanagi are trying to take control of the DCS building! Let A(t) and S(t) be the amount of territory (in square meters) each of them cover at a given time, respectively. These values change dynamically according to the system of differential equations with initial conditions A(0) = S(0) territory. A' = wA+S+ et S' yA+S+t 1. Assume these changes stop once someone runs out of Let (w,x,y,z) (1,-1,-1,1). Who eventually runs out of territory, and at what point in time does this happen? Suppose the second equation was S' = yA+ zS+ e² instead. Let (w, x, y, z) = (0.5, 1, 1, 2). Who eventually runs out of territory, and at what point in time does this happen?
Transcribed Image Text:Ayanokouji and Sakayanagi are trying to take control of the DCS building! Let A(t) and S(t) be the amount of territory (in square meters) each of them cover at a given time, respectively. These values change dynamically according to the system of differential equations with initial conditions A(0) = S(0) territory. A' = wA+S+ et S' yA+S+t 1. Assume these changes stop once someone runs out of Let (w,x,y,z) (1,-1,-1,1). Who eventually runs out of territory, and at what point in time does this happen? Suppose the second equation was S' = yA+ zS+ e² instead. Let (w, x, y, z) = (0.5, 1, 1, 2). Who eventually runs out of territory, and at what point in time does this happen?
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