In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$, one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are

Given the matrix:

For eigenvalue $\lambda = 1$, the corresponding eigenvectors satisfy $(A - I)X = 0$:

From row 1:

From row 3:

Letting $z = \alpha$ (where $\alpha \neq 0, \alpha \in \mathbb{R}$):

Thus, the set of eigenvectors is $\{\alpha(-4, 2, 1) \mid \alpha \neq 0, \alpha \in \mathbb{R}\}$.