Inverse Systems: a$)$ Given a system S$1,$ explain what is the meaning of its inverse system. Be specific. $(3$ marks$)$ b$)$ Given a causal LTI system with LCCDE $[]+0\mathrm{.}5[1]=[]$ Find its Transfer function H$($z$).$ Be sure to state the ROC. $(2$ marks$)$ c$)$ Is this system stable? Justify your response. $(2$ marks$)$ d$)$ Find the transfer function of its inverse system. Call it HI$($z$).$ Be sure to state the ROC. $(4$ marks$)$ e$)$ Find the LCCDE of the inverse system. $(2$ marks$)$ f$)$ Find the impulse response hI$[$k$]$ of the inverse system. $(2$ marks$)$ g$)$ Is the inverse system stable? Justify your response. $(2$ marks$)$