Question: Find a basis for each generalized eigenvalue of consisting of a union of disjoint cycles of generalized eigenvalues. Then find a Jordon canonical form of . The matrix given is:

[11 -4 -5

21 -8 -11

3 -1 0]

My attempt: So the characteristic matrix is , which gives with multiplicities of respectively. Then and . Specifically, and . I managed to find a basis for , which is

[1

3

0]

But when I tried it for , I got:

[9 -4 -5

21 -10 -11

3 -1 -2]^2 x = 0

which provides a basis with dimension 3, which makes no sense. Any hints, please? Thanks!