> 
> *Let $T: \mathbb{R}^2 \to \mathbb{R}^3$ and $T(-2,3)=(-1,0,1)$ and $T(1,2)=(0,-1,0)$.*
> 
> 
> *Obtain the canonical matrix of $T$ and the transformation $T(x,y)$.*
> 
> 
> 

How I obtain the canonical matrix of a transformation?

This is the "official answer": It's hard to see but maybe it gives a light on what was done. But I couldn't understand it.

![enter image description here](https://i.stack.imgur.com/CWVAZ.png)