For matrix $A = \begin{bmatrix} 2 & 1 & 1\\ 1 & 2 & 1\\ 1 & 1 & 2 \end{bmatrix}$, the characteristic polynomial of $A$ is $\charpoly{A}{x} = (4-x)(1-x)^2$. Find the eigenvalues and corresponding eigenspaces of $A$.