A linear language is one for which there exists a linear grammar
[A linear grammar is a grammar in which at most one variable can occur on the right side of any production, without restriction on the position of this variable. Clearly, a regular grammar is always linear, but not all linear grammars are regular].
Let $L$ be any linear language not containing $λ$. Show that there exists a grammar $G = (V, T,S, P)$ all of whose productions have one of the forms
$A\rightarrow aB,$
$A\rightarrow Ba,$
$A\rightarrow a,$
where $a∈ T$ , $A, B∈ V,$ such that $L = L (G)$.