An underdetermined system is a system of linear equations having fewer independent equations than unknowns. For a consistent
system 
over a field 
, with 
unknowns and 
, the solution set is an affine subspace of dimension
.
If 
is a finite field with 
elements, the solution set has 
elements; if 
is infinite, it contains infinitely many solutions.
Underdetermined System
See also
Linear System of Equations, Null Space, Overdetermined System, RankExplore with Wolfram|Alpha
References
Strang, G. Linear Algebra and Its Applications, 4th ed. Belmont, CA: Brooks/Cole, 2006.Cite this as:
Weisstein, Eric W. "Underdetermined System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnderdeterminedSystem.html