Consistency of 6x5 Linear Systems: A Scientific Perspective

Click For Summary

Homework Help Overview

The discussion revolves around the consistency of a system of 6 equations with 5 unknowns, specifically questioning whether such a system can always be consistent. Participants explore the implications of Gaussian elimination and the definitions of consistency in linear systems.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the definition of consistency in the context of linear equations and whether a system can yield contradictory results, such as 0=1, after applying Gaussian elimination. Others provide examples to illustrate potential inconsistencies.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Clarifications about the number of equations and unknowns have been made, and there is an acknowledgment of assumptions regarding the problem setup.

Contextual Notes

There is a noted confusion regarding the phrasing of the problem, specifically the distinction between equations and unknowns, which may affect the interpretation of consistency.

EvLer
Messages
454
Reaction score
0

Homework Statement



is every system of 6 equations and 5 unknowns consistent?

I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.
Thanks
 
Physics news on Phys.org
EvLer said:
is every system of 6 equations and 5 unknowns consistent?

I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.

What does it mean for a system of linear equations to be consistent? Does your answer agree with the definition?
 
A trivial example:

x1 + x2 + x3 + x4 + x5 = 1
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0

Does this system have a solution?

Edit: I forgot to add the 6th equation. The question remains unchanged.
 
Last edited:
thanks.
ps: sorry, perhaps I made a mistake: 6 equations IN 5 unknowns.
 
That was what everyone assumed you meant, that is what radou gave.
 

Similar threads

Find the solutions of the system, for all λ
  • · Replies 7 ·
Replies
7
Views
2K
Proving stability of linear system equations
  • · Replies 2 ·
Replies
2
Views
1K
Solution Sets of Linear Systems
  • · Replies 14 ·
Replies
14
Views
3K
Linear homogenous system with repeated eigenvalues
  • · Replies 2 ·
Replies
2
Views
2K
Linear Independence of \cos x, \cos (x+2), \sin (x-5)
  • · Replies 6 ·
Replies
6
Views
2K
Solving a system of linear equations
  • · Replies 28 ·
Replies
28
Views
3K
Trouble understanding linear transformations in this context
  • · Replies 3 ·
Replies
3
Views
2K
The consistency of linear systems
  • · Replies 11 ·
Replies
11
Views
3K
Solving Systems of Linear Equations (Echelon Matrices)
  • · Replies 2 ·
Replies
2
Views
2K
Linear Algebra - Linear (in)dependence of a set
  • · Replies 2 ·
Replies
2
Views
2K