Systems of Homogeneous Linear Differential Equations

[DODGEVIPER13]

Homework Statement

I uploaded the problem statement please see attachment for original problem. The problem number is 4.

Homework Equations

The Attempt at a Solution

For clarity I uploaded what I have done please see the attachment with my work on it. I am not sure if I am doing it right or not. If I am doing the problem correctly am I finished or should I do more? Just so you know I am doing the part from where it says suppose we are given a system of differential equations to the part where it says then finding the corresponding eigenvectors V.

 

[HallsofIvy]

You've got me confused! #4 on the page you give (there are NO "problems". This looks like a review sheet telling you what concepts you should review, not individual problems.) refers to $y_1'= y_1+ 2y_2$ and $y_2'= 3y_1+ 2y_2$ while your work sheet deals with $y_1'= 5y_1+ 6y_2$ and $y_2'= 2y_1+ y_2$.

 

[DODGEVIPER13]

I uploaded the incorrect thing sorry and I am confused as well but I can tell you I am not working the y1(prime) = y1+2y2 and y2(prime) = 3y1+2y2 part of it. I am trying to work out the general concepts listed. I am going to redo it and resubmit it.