Exercise 0.1.16 a) Determine whether the following subsets are subspace (giving reasons for your answers). (i) U = {A € R2x2|AT = A} in R2x2. (R2x2 is the vector space of all real 2 × 2 matrices under usual matrix addition and scalar-matrix multiplication.) ero ma (ii) W = {(x, y, z) = R³r ≥ y ≥ z} in R³. b) Find a basis for U. What is the dimension of U? (Show all your work by explanations.) c) What is the dimension of R2x2? Extend the basis of U to a basis for R2x2.