Checking Solution for c1, c2, and c3=0

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Discussion Overview

The discussion revolves around solving a system of equations derived from a polynomial expression involving coefficients c1, c2, and c3, specifically aiming to verify that the only solution is c1=c2=c3=0. The scope includes mathematical reasoning and problem-solving techniques related to linear algebra.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a polynomial equation and derives three equations from specific values of t.
  • Another participant suggests simply solving the system of equations for c1, c2, and c3.
  • A participant expresses difficulty in solving the system, indicating a lack of confidence in their skills.
  • Another participant points out that there are three equations for three unknowns, implying that a solution should be attainable.
  • A participant mentions their familiarity with solving similar problems using matrices but struggles with the current setup.
  • One participant suggests interchanging equations to facilitate solving the system, asserting that this will not change the solution.
  • A later reply indicates that the original poster has resolved their issue, expressing gratitude.

Areas of Agreement / Disagreement

Participants generally agree that the problem involves solving a system of equations, but there is no consensus on the specific methods or approaches to achieve this. The discussion reflects varying levels of confidence and understanding among participants.

Contextual Notes

Some participants express uncertainty regarding their mathematical skills and the specific techniques needed to solve the equations, indicating potential limitations in their understanding of linear algebra concepts.

gunnar
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I have :
c1(t+1) + c2(t^2 + 2) + c3(t^2 -t) = 0 for all t.
by specifying different values of t. I get
t=-1: 3c2 + 2c3=0
t=0: c1+2c2 =0
t=1:2c1 + 3c2 =0

How can I check that the only solution is c1=c2=cc3=0 ?
 
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Simply solve the system of equations you've just made for c1,c2,c3.
 
that's the problem I don't know how. I know it's simple but I just can't figure it out?
 
You have 3 equations in 3 unknowns; you've seen that before?
 
I've done this when I have a matrix in reduce or reduce echelon but then I only have x1 in one linem here I have c1 in 2nd and 3rd row and it's there I am stuck. I admit I'm not very good at this. If you possibly can would you be so kind to lead my on with this problem?? :smile:
 
Why don't you just interchange line 1 and line 3?
Interchanging "topmost equation" with "bottom-most equation" can't possibly change the solution, or what?
 
I got it. Thanks a lot :smile:
 

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