underbestemte

Underbestemte refers to a mathematical concept, primarily used in linear algebra, to describe a system of linear equations that has infinitely many solutions. This occurs when the number of variables in the system is greater than the number of independent equations. In such a scenario, it's impossible to find a unique value for each variable. Instead, the solutions can be expressed as a set of related values, often dependent on one or more free variables. Geometrically, an underdetermined system represents lines or planes that intersect in a way that creates a line, plane, or higher-dimensional space of solutions, rather than a single point. This is in contrast to determined systems, which have a unique solution, and overdetermined systems, which have no solution. Identifying whether a system is underdetermined is crucial for understanding the nature of its solutions and for choosing appropriate methods for solving it.