Unique Solution for Tx=y in R(T) when T is injective

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Discussion Overview

The discussion revolves around the conditions under which the equation Tx = y has a unique solution, specifically focusing on the case where T is an injective linear transformation from vector space V to vector space W.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that the equation Tx = y has a unique solution if and only if T is injective.
  • Another participant questions the clarity of the initial post and asks for details on what has been attempted to prove the statement.
  • A participant expresses a desire for only the idea behind the proof, indicating a preference for conceptual discussion over detailed steps.
  • There is a challenge to the clarity of communication, with one participant requesting a more straightforward response to the question posed about prior attempts.
  • A participant indicates that they have made some progress but does not specify what that entails.
  • Another participant expresses frustration over the lack of clarity and engagement with the questions posed for clarification.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple requests for clarification and differing levels of understanding regarding the proof and its requirements.

Contextual Notes

There are limitations in the clarity of communication and the specifics of the proof attempts, which may affect the progression of the discussion.

juaninf
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Supposse that y \in{R(T)}, T\in{L(V,W)} the equation Tx=y, have unique solution if only and if T is injectiva
 
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What have you tried? Do you know how to prove if and only if statements?
 
yes, first left after right, i want only idea,
 
? "first left after right" means nothing to me. Please answer Mark44's question, "What have you tried?".
 
I maked this
 
If you aren't going to answer questions asked to clarify your post, I see no reason to continue this.
 

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