Suppose U = {(x, x, y, y) = F4 : x, y = F}. Find a subspace W of F such that F = U W. CHAPTER 1 Vector Spaces Suppose U = {(x, y, x+y.x-y, 2x) e FS: x, y = F}. Find a subspace W of F5 such that F5 = U + W. Suppose U = {(x,y.x+y.x-y.2x) E FS: x, y = F}. Find three subspaces W, W2, W3 of FS, none of which equals {0} Chat FSU W W W3. Prove or give a counterexample: if U1, U2. W are subspaces of V Chat then U = U. V = UW and V = U W. A function f: RR is called even if f(-x) = f(x) for all x E R. A function f: RR is called odd if f(-x)=-f(x) for all x R. Let Ue denote the set of real-valued even functions and let Uo denote the set of real-valued odd functions on R. Show RR=UU.