Thank you!

Problem 1. Let V be a vector space. Use the universal property of the tensor product V Q V to construct a linear map f : Vo V -> V @ V such that ker(f) contains v @ v for every v E V. That is, define a bilinear map V : V x V -> VOV (you must show your map is bilinear) and show that the corresponding linear map f has v Q v E ker(f) for every v E V