(Solved): \[ A=\left[\begin{array}{ccc} 1 & -1 & -1 \\ 2 & 4 & 2 \\ -1 & -1 & 1 \end{array}\right] \] has ei ...

\[ A=\left[\begin{array}{ccc} 1 & -1 & -1 \\ 2 & 4 & 2 \\ -1 & -1 & 1 \end{array}\right] \] has eigenvalue \( \lambda=2 \) repeated three times. It has an eigenspace of dimension 2 and one generalized eigenvector. A. Find a basis for the 2-eigenspace: \[ \{[-],[-]\} \] B. Find a generalized 2-eigenvector, as well as the eigenvector it generalizes: \[ \overrightarrow{\boldsymbol{w}}=[=] \text { generalizes the 2-eigenvector } \overrightarrow{\boldsymbol{v}}=[-] \]