Suppose your colleague built a system of transmitters that is not well designed $($ie$.$ Nul $($H$)+\{0\}).$ Your boss tells you to fix this error by simply tearing down some of the transmitters. Can you do so without changing what kind of message can be received? If so$,$ how do you determine the transmitters you have to tear down. $($Hint: how do you find a basis of Col$($H$)?)+($h$)$ Oh no$,$ a tornado destroved the n transmitters! Your company built n new transmitters and tells you that the new channel matrix is H$\text{'}.$ You are told that the column space of His equal to the column space of H$\text{'}.$ How can you check that this claim is true?