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EDIT3:

Hello,

I need help with the last question on my assignment, but I'll post the previous ones if that will of help for you:

b)Determine (analytical) eigenvalues ​​and eigenvectors of A and from there an eigenbasis (Is the choice of eigenbasis unique?)

c)Express x(0) in the system of the eigenbasis from b) by solving the corresponding system of equations.

d)Determine the analytical solution for x(t) by combining a), b ) and c)

e) There are three different scenarios for the solution depending on the values ​​of the constants r and s:

1. r + s < 1
2. r + s = 1 3 ) r + s > 1

For each case , sketch (paper) / draw ( Mathematica) solution as a function of time t (Parametric plot / phase portraits) with exposed eigenvectors in the same figure (three figures in total) . Give an interpretation of the solution in each case what it means in terms of upgrading/disarmament. Vary the values ​​of the constants r and s and study how the solution changes (Mathematica) (you can assume that r > s)

So I'm having problem understanding e). Is my case exactly what Bob Hanlon has been plotting? (Sorry if I don't get it, I'm quite new when it comes to Mathematica so everything isn't clear for me). I have solved a) b) c) and d), and it's only e) that I want guidelines on how to solve/what I should think about.

Thanks!:)

EDIT3:

Hello,

I need help with the last question on my assignment, but I'll post the previous ones if that will of help for you:

b)Determine (analytical) eigenvalues ​​and eigenvectors of A and from there an eigenbasis (Is the choice of eigenbasis unique?)

c)Express x(0) in the system of the eigenbasis from b) by solving the corresponding system of equations.

d)Determine the analytical solution for x(t) by combining a), b ) and c)

e) There are three different scenarios for the solution depending on the values ​​of the constants r and s:

1. r + s < 1
2. r + s = 1 3 ) r + s > 1

For each case , sketch (paper) / draw ( Mathematica) solution as a function of time t (Parametric plot / phase portraits) with exposed eigenvectors in the same figure (three figures in total) . Give an interpretation of the solution in each case what it means in terms of upgrading/disarmament. Vary the values ​​of the constants r and s and study how the solution changes (Mathematica) (you can assume that r > s)

So I'm having problem understanding e). Is my case exactly what Bob Hanlon has been plotting? (Sorry if I don't get it, I'm quite new when it comes to Mathematica so everything isn't clear for me). I have solved a) b) c) and d), and it's only e) that I want guidelines on how to solve/what I should think about.

Thanks!:)