Difficult# Orthogonality of Distinct Eigenspaces of a Symmetric Matrix

LINALG-Q0GUEN

Consider the following matrix:

$$A=\begin{bmatrix}2&1&-1\\\ 1&2&-1\\\ -1 & -1& 2\end{bmatrix}$$

If $u, w$ are non-zero vectors such that $Au=4u$ and $Aw=w$, then which of the following statements are true.