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The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are)

1. $(0,0, \alpha)$
2. $(\alpha, 0,0)$
3. $(0,0,1)$
4. $(0, \alpha, 0)$