General Solution To Three Simultaneous Equations

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Discussion Overview

The discussion revolves around the general solution to three simultaneous equations, focusing on the methods and challenges involved in solving such systems. Participants explore various approaches, including matrix inversion and Gaussian elimination, while addressing the specifics of the equations presented.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant submits a general solution to a specific set of three equations in three unknowns, inviting review and comment.
  • Another participant questions the generality of the solution, noting the presence of zeros on the diagonal of the matrix involved and suggesting familiarity with matrix inversion.
  • A third participant agrees with the observation that the solution is general for a specific case and expresses a belief that there might be simpler methods for solving the equations.
  • One participant mentions that Gaussian elimination is a well-known method for solving systems of linear equations and highlights the need for pivot swapping to avoid division by zero in the general case.
  • A participant comments on the ease of typesetting the equations using LibreOffice Math, indicating that it was simpler than manual writing.

Areas of Agreement / Disagreement

Participants express differing views on the generality of the proposed solution, with some agreeing that it is specific rather than general. The discussion includes multiple perspectives on solving the equations, indicating that no consensus has been reached on the best approach.

Contextual Notes

Participants note limitations related to the specific nature of the equations and the implications of having zeros on the diagonal of the matrix, which may affect the methods used for solving them.

DavidZuccaro
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I herewith submit for reference, review and comment the general solution to 3 simultaneous equations as follows:

sim1.png

sim2.png

sim3.png
 
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Lot of work plus a lot of typesetting !
I do notice that you have written down a general solution for a not so general set of three equations in three unknowns.
Are you familiar with things like inverting a 3x3 matrix? Your matrix has zeros on the diagonal.
 
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BvU said:
Lot of work plus a lot of typesetting !
I do notice that you have written down a general solution for a not so general set of three equations in three unknowns.
Are you familiar with things like inverting a 3x3 matrix? Your matrix has zeros on the diagonal.

I agree, it's a general solution to a specific set of equations :)

Thanks, I thought that there was a simpler way of solving those.
 
There are several ways of solving a system of linear equations. The most well-known is the "Gaussian elimination" (https://en.wikipedia.org/wiki/Gaussian_elimination). In the general case, you probably need to do a "pivot swapping" for each column to ensure that you do not divide by zero.
 
The typesetting was not a problem -- all handled by LibreOffice Math. It was easier than writing.
 

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