What is examples of languages to prove the inclusions between families of languages generated by matrix grammars?
To my knowledge, it is an open problem whether the inclusion (c) above
is strict. Some (baby) steps toward solving this problem can be found in

"Toward Understanding the Generative Capacity of Erasing Rules in Matrix Grammars", IJFCS 2011, http://dx.doi.org/10.1142/S0129054111008118

"On Erasing Productions in Random Context Grammars", ICALP 2010, http://dx.doi.org/10.1007/978-3-642-14162-1_15

"A Sufficient Condition for Erasing Productions to Be Avoidable", DLT 2011.
http://link.springer.com/chapter/10.1007%2F978-3-642-22321-1_39