Solving a Matrix System: a^2 - 1, a, b

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Discussion Overview

The discussion revolves around solving a matrix system involving variables a, b, and c, with a focus on determining conditions for consistency. Participants explore the transformation of the matrix into a system of equations and the implications of consistency in the context of the equations derived from the matrix.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant seeks assistance in solving a matrix for variables a, b, c, and d, emphasizing the need for the system to be consistent.
  • Another participant suggests transforming the matrix back into a system of equations to facilitate solving.
  • A participant provides the equations derived from the matrix, indicating the relationships between the variables x, y, and z.
  • There is a discussion about the meaning of consistency in the context of the matrix system, with one participant affirming that it relates to the ability to solve the system.
  • One participant expresses frustration at being unable to solve the system, indicating they are stuck.
  • A question is raised regarding the value of z needed for consistency, prompting further exploration of its possible values.
  • Another participant proposes multiple potential values for z, suggesting it could be -1, 1, 3, or -3.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific values of z that would ensure consistency, and the discussion remains unresolved regarding the conditions for the matrix system.

Contextual Notes

The discussion does not clarify the assumptions regarding the values of a and b, nor does it resolve the mathematical steps necessary to determine consistency fully.

lolimcool
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hey anyone want to help me start solving this matrix for a b c d where the system will be consistent

[1 -2 4 | 7 ]
[0 (a^2 - 1) a | 3 ]
[0 0 b | -3]
 
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You can start by transforming this matrix back into a system of equations of x, y, z. What system do you obtain?
 
x -2y + 4z = 7
0 (a^2 -1)y + az = 3
bz = -3
 
What does it mean to be consistent? It means that you can solve it, right? ...
 
yeah, i know I've tried to solve it, just keep getting stuck
 
What does z need to be in order to be consistent? (look at the last equation!)
 
cant z be either -1, 1, 3, -3 ?
 

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