Unique solution of an overdetermined system

  • Thread starter Thread starter Shaybay92
  • Start date Start date
  • Tags Tags
    System
Click For Summary
To determine the number of solutions in a consistent linear system with more equations than unknowns, assess the number of independent equations. A consistent system can have either one solution or infinitely many solutions, but cannot have more independent equations than variables. The relationship between the number of variables (n) and independent equations (m) is crucial, where n must be greater than or equal to m. The number of free variables is calculated as n minus m. Row-reducing the coefficient matrix reveals the number of independent equations through the count of non-zero rows.
Shaybay92
Messages
122
Reaction score
0
If I want to know how many solutions a consistent linear system with more equations than unknowns has, how do I tell? Obviously there is either 1 solution of infinite solutions. Can you have a free variable in this case? I'm confused how to find out whether a system will give a unique solution.
 
Physics news on Phys.org
You need to determine how many independent equations there are. If the system really is consistent, then there must be no more independent equations than unknown variables. That is, if n is the number of variables and m is the number of independent equations, then n\ge m. The number of free variables is n- m.

If you write the coefficient matrix for the system and row-reduce, the number of independent equations is the number of non-zero rows.
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

MHB Solving Systems of Six Equations with Nine Variables
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Do Planes Intersect in Various Linear Systems?
  • · Replies 6 ·
Replies
6
Views
2K
Is it worse an over or an under determined system of linear equations?
  • · Replies 15 ·
Replies
15
Views
8K
High School What unique contributions to math did linear algebra make?
  • · Replies 19 ·
Replies
19
Views
4K
Underdetermined vs Overdetermined Systems
  • · Replies 3 ·
Replies
3
Views
3K
MHB Relationship between three planes
  • · Replies 5 ·
Replies
5
Views
2K
Why would a solution not exist for an overdetermined system?
  • · Replies 6 ·
Replies
6
Views
9K
Undergrad True or False: A Linear System Must Have a Unique Solution
  • · Replies 1 ·
Replies
1
Views
1K
MHB Linear system of equations: Echelon form/Solutions
  • · Replies 3 ·
Replies
3
Views
1K
Linear Algebra uniqueness of solution
  • · Replies 6 ·
Replies
6
Views
1K