Formal languages: constructing * for a linear set
Hint. It suffices to observe that if $L = \{ v_0 + c_1v_1 + c_nv_n \mid c_1, \dotsm, c_n \in \mathbb{N}\}$, then $L^* = \{ c_0v_0 + c_1v_1 + c_n  v_n \mid c_0, \dotsm, c_n \in \mathbb{N}\}$.