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

[juaninf]

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

 

[Mark44]

What have you tried? Do you know how to prove if and only if statements?

 

[juaninf]

yes, first left after right, i want only idea,

 

[HallsofIvy]

? "first left after right" means nothing to me. Please answer Mark44's question, "What have you tried?".

 

[juaninf]

I maked this

 

[HallsofIvy]

If you aren't going to answer questions asked to clarify your post, I see no reason to continue this.