How to identify which eigenvectors correspond to generalized eigenvectors?
Solution 1:
Yes, there is. Note that$$A.(a,b,c,d)-2(a,b,c,d)=(-a+d,b-c,-a+d,b-c).$$This is a vector for which the first coordinate is equal to the third one and the second coordinate is equal to the fourth one. Neither $e_1$ nor $e_2$ have this form. But $e_3$ has.