1. Consider the field F2 = {0,1}, with addition defined by a+b = (a + b)mod2 and multiplication defined by ab = (ab)mod2. Let V be the vector space over F2 consisting of all ordered pairs (v, w) where v, w F2. How many linear transformations are there from V to itself?

2. Consider the complex vector space C2. Let U be the subset of C2 consisting of all vectors of the form (a + bi, b ai), where a and b are real numbers. Show that U is a subspace of C2.