How do find the rank of the given matrix depending on parameters $a, b \in \mathbb{Z}\_{7}$?

$$ A\in Mat\_{3,4}(\mathbb{Z}\_{7}), A=\begin{pmatrix} \overline{2} &b &\overline{1} &\overline{3} \\ \overline{-3} &\overline{3} b & \overline{2} a& \overline{0}\\ a & \overline{4} -a & \overline{-3} &\overline{1} +\overline{2} b \end{pmatrix}$$

I have found matrix rank by reducing matrix to echelon form, but there were no parameters involved in those questions, even more, two. I've spent days trying to figure out a solution by different methods (e.g by changing (-3) to 4 [they both give the same reminder when divided with 7] and then performed row operations, but it just did not worked out since i did not manage to reduce “a” to 0 etc. Then I started wondering whether I should just start by letting a/b equal to zero and watch different cases separately and reduce them to a desired form separately? I appreciate your help and explanations.