Are Coupled Linear Equations Always Solvable Analytically?

  • Context: Graduate 
  • Thread starter Thread starter KFC
  • Start date Start date
  • Tags Tags
    Set
Click For Summary

Discussion Overview

The discussion centers on the solvability of a set of coupled linear equations, specifically whether such equations can always be solved analytically. The scope includes theoretical considerations and potential methods for solving the equations presented.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether all sets of coupled equations are analytically solvable, presenting a specific set of equations as an example.
  • Another participant notes that there are five equations with five unknowns and suggests that the last equation can be divided by one of the variables.
  • A later reply reiterates the five equations and five unknowns and recommends the Gauss-Jordan elimination method as a potential solution approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solvability of the equations. There are differing views on the applicability of analytical methods and the specific approach to take.

Contextual Notes

There are potential limitations regarding the assumptions made about the constants in the equations and the conditions under which the proposed methods may be applicable.

Who May Find This Useful

This discussion may be of interest to those studying linear algebra, particularly in the context of solving systems of equations, as well as individuals exploring analytical methods in mathematics.

KFC
Messages
477
Reaction score
4
I wonder if all coupling set of equations are not solvable analytically? I have a equation set as follows

y1 = a1*y1 + c1*y2;
y2 = a2*y2+ b2*y1 + c2*y3;
y3 = a3*y3+ b3*y2 + c3*y4;
y4 = a4*y4+ b4*y3 + c4*y5;
y5 = a5*y5+ b5*y4;

a's, b's and c's are constant. So is there any way to solve these equations?
 
Last edited:
Physics news on Phys.org
5 equations 5 unknowns. not to mention your last equation can be divided by y5
 
dacruick said:
5 equations 5 unknowns. not to mention your last equation can be divided by y5

Sorry, some typo. I correct the equations.
 
KFC said:
Sorry, some typo. I correct the equations.
You still have 5 equations and 5 unknowns. Look at Gauss-Jordan elimination, it's an algorithm that will spit out a solution.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 7 ·
Replies
7
Views
9K
  • · Replies 2 ·
Replies
2
Views
5K