Can Gaussian Elimination Solve a System with Identical Equations?

Click For Summary

Discussion Overview

The discussion centers on whether Gaussian elimination can be used to solve a system of equations that consists of identical equations. The focus is on the implications of having multiple identical equations in terms of solutions in a three-dimensional space.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that Gaussian elimination cannot yield a unique solution for the system of identical equations.
  • Another participant counters that while there is not a single unique solution, there are infinitely many solutions represented by points on a plane defined by the equation 2x + 3y + 3z = 7.
  • A third participant expresses agreement with the viewpoint that there are infinite solutions, reinforcing the idea that all three equations represent the same plane in three-dimensional space.

Areas of Agreement / Disagreement

Participants disagree on the ability of Gaussian elimination to provide a unique solution, with some asserting it cannot while others argue that it can yield infinitely many solutions.

Contextual Notes

The discussion does not resolve the implications of using Gaussian elimination on identical equations, nor does it clarify the mathematical steps involved in the process.

Biloon
Messages
6
Reaction score
0
2x+3y+3z=7
2x+3y+3z=7
2x+3y+3z=7

Using Gaussian Elimination... is it possible to find the value of x,y,z with three similar equation?
 
Physics news on Phys.org
absolutely not
 
Actually it is. Not ONE value of course, there are an infinite number of (x, y, z) triples that satisfy 2x+ 3y+ 3z= 7 and you really only have one equation. In 3 dimensions 2x+ 3y+ 3z= 7 is the equation of a plane. Any (x,y,z) point on that plane satisfies that equation (and so, all "three" of your given equations).
 
Haha, I was thinking the same thing.
 

Similar threads

Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 26 ·
Replies
26
Views
5K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
3K