An overdetermined system is a set of equations or constraints that has more equations than unknown variables. This means that there are more conditions to be satisfied than there are variables to be determined.
Yes, it is possible for an overdetermined system to have a unique solution. This can happen when the extra equations are not independent and can be derived from the other equations in the system. In this case, the system is considered to be consistent and has a unique solution.
The unique solution of an overdetermined system is typically calculated using methods such as least squares or matrix inversion. These methods involve finding the best possible solution that satisfies the given equations, even if it does not satisfy all of them perfectly.
Yes, overdetermined systems have many real-world applications, particularly in fields such as engineering, physics, and economics. They are often used to model complex systems with more constraints than unknown variables, such as in optimization problems or data analysis.
If an overdetermined system does not have a unique solution, it is considered to be inconsistent. This means that there is no set of values that can satisfy all of the equations in the system. In this case, the system is either under-constrained or contradictory, and it is not possible to find a unique solution.