Can every linear grammar be converted to Greibach form? Can every linear grammar be converted to a linear Greibach normal form, a form in which all productions look like $A \rightarrow ax$ where $a \in T$ and $x \in V \cup \{\lambda\}$?

($T$ is the set of terminals, $V$ is the set of non-terminals, $\lambda$ is the empty sequence.)
The more general answer is:

Blum and Koch showed a polynomial time transformation such that any context-free grammar can be converted to Greibach form.

Since a linear grammar is a special case of Context-free grammar, the answer is yes.



A simpler transformation:


Any rule $X \rightarrow a_1 a_2 \cdot a_k Y$ you transform them in $k$ rules: 


$X\rightarrow a_1 X_1Y$.
$\cdots$
$X_{i-1}\rightarrow a_{i}X_i$
$X_{k-1}\rightarrow a_{k}Y$

Any rule $X \rightarrow a Y b$ should be transformed in two rules


$X \rightarrow a Y Y_1$.
$Y_1 \rightarrow b$



where the capital letters belong to $V$ and the small letters to the alphabet (terminals).