The question asks to find the solution of the system x'(t)=Ax(t)

given my A is

After finding my det(

=>

I found three real roots:

Now starting with the first root equal to -10 and plugging into the det matrix

*

=

I found my U1 to be <2, 0, -1>

Now I'm confused what to do with the last two lambdas, I get the feeling that there should be more than just two Cn's

My question is can someone show me how to solve for u2 and u3 (if there is a u3), the way my textbook explains solving for eigenvectors is not helping very much considering the questions are getting harder and the method I've been using doesn't seem to be working.