Over-determined and Under-determined systems How do I show that a system is both over-determined and under-determined? I am supposed to come up with a matrix that satisfies both but am not really sure I understand what types of equations would satisfy these criteria. If anyone could give me an example and maybe a format to go by, I would appreciate it. 

I believe that, as pointed out in Overdetermined and underdetermined systems of equation put simply, thinking of the equations in a system making up a set of requests (equations) to a certain number of people (unknowns) is helpful to understand why systems can be overdetermined or underdetermined in the first place.
In your specific case, imagine to have 3 people, all waiting for a command from you. Finally, you speak and say:


*

*Bob, go fetch a bottle of water

*Bob, help me paint the house

*Lisa, do your homework


This is a real world example of a system that is both under and overdetermined. What makes it underdetermined is the fact that you had 3 people in front of you, and only addressed 2 of them, whereas giving conflicting commands to Bob makes it an overdetermined one.
