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. 

An over-determined system is a system of equations that has more equations than unknowns (e.g. three equations and two unknowns).  
An under-determined system is a system of equations that has more unknowns than vectors (e.g. three unknowns and two equations).
The combination of the two leads to the critical case which is when you have the same number of equations as you do unknowns.  The best case scenario of this would be to start in reduced row echelon form and work your way backwards to come up with an example of such a matrix.
