I don't understand this definition.

In a linear transformation, 0,0) \to (0,0)" alt="f0,0) \to (0,0)" />. If 0,0)" alt="f0,0)" /> (the "to" symbol with the "not" diagonal cross in it) (0,0), the mapping is not a linear transformation.

Now I have to determine if each mapping that moves (x,y) to the given point is a linear transformation. I don't get how it works.

Why is moving (x,y) to (0,x) is a linear transformation and moving it to (x,-1) is not?

Another question I don't get.

Given the linear transformation , determine the matrix of the linear transformation which moves points (1,0) and (0,1) to points (1,2) and (3,4), respectively.

How do you get the answer ?