Final answer:
A linear system can have none, one, or infinitely many equilibrium solutions, and a non-linear system can have a varied number of equilibriums, not just two or three. Types of equilibrium include stable, unstable, and neutral, applicable to both linear and non-linear systems.
Step-by-step explanation:
The statement that a linear system with constant coefficients has one equilibrium solution while a non-linear system has two or three equilibriums is false. Linear systems can have none, one, or infinitely many equilibrium solutions depending on the system. The equilibrium is the point where the net force and the net torque on the system are zero. A linear system is typically represented by linear equations where the sum of vector components or the choice of pivot point does not change the conditions for equilibrium. Conversely, non-linear systems, described by non-linear equations, can have multiple equilibriums, and the number can vary widely, not limited to two or three. For example, a chemical equilibrium is dependent on the equilibrium constant (K), and systems can exist where K is very large or very small, indicating a predominance of products or reactants, respectively, at equilibrium.
There are also different types of equilibria such as stable, unstable, and neutral equilibrium, which are determined by the behavior of the system when it is perturbed. Stable equilibrium will return to its original position after being displaced, unstable equilibrium will move away, and neutral equilibrium will stay in its new position. These types can occur in both linear and non-linear systems.