1. For a map f : V ?? W between vector spaces V and W to be alinear map it must preserve the structure of V . What must oneverify to verify whether or not a map is linear?
2. For a map f : V ?? W between vector spaces to be anisomorphism it must be a linear map and also have two furtherproperties. What are those two properties? As well as giving thenames of the properties, explain what the names mean.
3.Every linear transformation is an isomorphism, but theisomorphism f : x y ?? x y is not a linear transformation. Why
