$($c$)$ In terms of signals, what is Co$!($H$)?($d$)$ If the signal x belongs to the nullspace of H$,$ what signal y will be received?$($e$)$ In a well designed system, what do you want Nul$($H$)$ to be$?$ What does that tell you about the columns of H$?+($f$)$ If you add one more transmitters, how does H change and how does the column space of H change? How do you have to choose the new transmitter in order to be able receive more messages?