Problem 1. Let V be a vector space over a field F. Denote by dim(V) the dimension of V over F. (a) Let V C. Show that the vectors v = = What is dime(V)? (1, 1) and v = (i, 1) are a basis of V over C. (b) The vector space V scalar multiplication to RC C. Find dim(V). (c) (Bonus problem, do not turn in!) Let V be a vector space over C. Show that dim (V) = 2 dimc (V). = C can also be viewed as a real vector space by restriction of the