Abstract: For any given complex number $\lambda$, this paper proved that there exists a
3 by 3 nonnegative matrix
\textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}.
The number 4 of zero entries here is the largest possible.

Key words: inverse eigenvalue, companion matrix , nonnegative matrices, inverse eigenvalue, companion matrix