$(1)($a$)$ Give an example of a consistent $3\backslash$times $5$ system so that the general solution has three

parameters, or explain why such a system can$$t exist. $($Be sure to provide justification

that your example has the properties required.$)$

$($b$)$ Give an example of a consistent $3\backslash$times $5$ system so that the coefficient matrix has rank $4,$ or

explain why such a system can$$t exist. $($Be sure to provide justification that your example

has the properties required.$)$

$($c$)$ Is it possible for a $3\backslash$times $5$ system to have a unique solution? What about a $5\backslash$times $3$ system?

Explain your answer with appropriate justification $($e$.$g$.$ citing theorems$/$results from the

reading or from class.$)$