Multiple choice

Which one of the following is an eigen vector of the matrix $\begin{bmatrix} \ 5 & 0 & 0 & 0 \ \ 0 & 5 & 0 & 0 \ \ 0 & 0 & 2 & 1 \ \ 0 & 0 & 3 & 1 \ \end{bmatrix}?$

  1. $\begin{bmatrix} \ 1 \\ \ -2 \\ \ 0 \\ \ 0 \\ \end{bmatrix}$
  2. $\begin{bmatrix} \ 0 \\ \ 0 \\ \ 1 \\ \ 0 \\ \end{bmatrix}$
  3. $\begin{bmatrix} \ 1 \\ \ 0 \\ \ 0 \\ \ -2 \\ \end{bmatrix}$
  4. $\begin{bmatrix} \ 1 \\ \ -1 \\ \ 2 \\ \ 1 \\ \end{bmatrix}$
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