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

(a) \(\begin{bmatrix} 1\\ -2\\0\\0 \end{bmatrix}\)                                    (b)    \(\begin{bmatrix} 0\\ 0\\1\\0 \end{bmatrix}\)

(c)    \(\begin{bmatrix} 1\\0 \\0\\-2 \end{bmatrix}\)                                  (d)    \(\begin{bmatrix} 1\\ 0\\1\\0 \end{bmatrix}\)