What is the difference between overdetermined and underdetermined systems?

The correct understanding of overdetermined systems is that they have more equations than unknowns, which can sometimes lead to contradictory solutions. In such systems, because there are more equations than variables, it is possible that the equations do not all consistently intersect at a single solution point. This situation arises particularly in scenarios where the equations represent constraints that do not agree with one another. As a result, the system may have no solution or may yield a solution that satisfies only a subset of the equations.

In contrast, underdetermined systems have fewer equations than unknowns, which typically leads to an infinite number of solutions, rather than contradictions. This distinction is crucial for understanding how different types of systems behave when trying to find solutions.

This highlights the importance of the relationship between the number of equations and unknowns in determining the nature of a system's solutions, particularly in engineering analysis and computation.