## Jordon Canonical Form

Question: Find a basis for each generalized eigenvalue of $L_A$ consisting of a union of disjoint cycles of generalized eigenvalues. Then find a Jordon canonical form $J$ of $A$. The matrix given is:
[11 -4 -5
21 -8 -11
3 -1 0]

My attempt: So the characteristic matrix is $f(x) = -(x+1)(x-2)^2$, which gives $x_1=-1,x_2=2$ with multiplicities of $1,2$ respectively. Then $dim(K_1) = dim(E_1) = 1$ and $dim(K_2)=2$. Specifically, $K_1 = N(T+I)$ and $K_2 = N[(T-2I)^2]$. I managed to find a basis for $K_2$, which is
[1
3
0]
But when I tried it for $K_2$, I got:
$N[(T-2I)^2]$
[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!