Linear Algebra: Lecture 19: subspace thms for LT and unique linear extension prop

Here I prove the fundamental theorems about subspaces and linear transformations, we also discuss the vector space structure of L(V,W) as well as the fact that L(V,V) forms an algebra with respect to composition. Finally I conclude with the linearly extending off a basis proposition. Notice, at 48:30 or so I incorrectly say c_i is a real number. Of course, I should say c_i is a vector in W for each i.