1. Fill in the blanks in the following definitions (a) (7 points) A linear transformation F from a vector space V to a vector space W is a function from V to W that satisfies (1) For all x and y in_ (2) For all x in, and all (b) (4 points) Let V be a vector space and X - [vi, , vkÅ a finite set of vectors in V. The set X is called a finite basis of V if it has the following two properties: (c) (7 points) If V is a subset of R", then V is a subspace of R" if it satisfies the following 3 conditions 2. If u, v 3. If cER and vt then then 2. Fill in the blanks in the following statements of results from the text (a) (4 points) If T: Rn â RTn is a linear transformation with associated matrix A, then the of A is the image T(e) for 1
