Homework 4

Rachael Steiner

5.1.10



In [3]:

    
addpath('../modules');



In [7]:

    
A = [0 2; 1 0];
eival(A)









    



ans =

    1.4142   -1.4142

One eigenvalue is positive and the other is negative, so it is neutrally stable.



In [9]:

    
A = [0 0; 0 -1];
eival(A)

Neutrally stable



In [10]:

    
A = [1 0; 0 1];
eival(A)

Unstable.



In [11]:

    
A = [0 1; -2 -3];
eival(A)









    



ans =

    -1    -2

Stable



In [13]:

    
A = [5 10; 1 -1];
eival(A)









    



ans =

    6.3589   -2.3589

neutrally stable



In [16]:

    
A = [3 -4; 1 -1];
eival(A)

Unstable



In [17]:

    
A = [-3 2; 1 -2];
eival(A)









    



ans =

    -1    -4

Stable



In [18]:

    
A = [5 2; -17 -5];
eival(A)









    



ans =

   0.0000 + 3.0000i   0.0000 - 3.0000i

does not exist



In [19]:

    
A = [-3 4; -2 3];
eival(A)

Neutrally stable



In [20]:

    
A = [4 -3; 8 -6];
eival(A)

Neutrally stable



In [23]:

    
A = [0 1; -1 -2];
eival(A)









    



ans =

    -1    -1

Stable