I think this slide is very intuitive. Based on some "common sense" people are more likely to say that the first one is a linear map even without the explicit definition of a "linear map". This way of teaching is more convincing and can help people remember the required properties more easily, compared with "just give the required properties and let students remember them". Some other slides also take the same idea.

I think this slide is very intuitive. Based on some "common sense" people are more likely to say that the first one is a linear map even without the explicit definition of a "linear map". This way of teaching is more convincing and can help people remember the required properties more easily, compared with "just give the required properties and let students remember them". Some other slides also take the same idea.