How do you solve for eigenvectors? I get the eigenvalues. Here is the problem.
[2 0 0
1 -1 -2
-1 0 1]
The characteristic polynomial is -x^3+2x^2+x-2 (obviously is lambda but I am using x for now)
eigen values are x1= -1
x2= 1
x3= 2
How would you do the eigenvectors?

Question

How do you solve for eigenvectors? I get the eigenvalues. Here is the problem.
[2 0 0
1 -1 -2
-1 0 1]
The characteristic polynomial is -x^3+2x^2+x-2 (obviously is lambda but I am using x for now)
eigen values are x1= -1
x2= 1
x3= 2 
How would you do the eigenvectors?

anonymous · Answer

Replace your eigenvalues, one at a time, for lambda in your (A-xI) matrix- where x is lambda. So you'll have 3 separate matrix equations, (A-xI) v = 0,  to solve for three different eigenvectors. You're almost there, just that one last step!