# Thread: True or False

1. ## True or False

Two eigenvectors corresponding to the same eigenvalue must be linear dependent.

2. I think it is true.

3. No, it's false. For example, the identity matrix $\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$ has 1 as its only eigenvalue. Both [1 0] and [0 1] are eigenvectors corresponding to eigenvalue 1 and are independent.