A flag is an increasing sequence of subspaces (with respect to subspace inclusion) of a finite-dimensional vector space V . Let {v1, v2, . . . , vn} be a sequence of linearly independent vectors in V . Show that setting U0 = {0} and Ui = span{v1, . . . , vi} for i = 1, . . . , n gives a flag for V . In other words, show that 0 U1 U2 Un V. Note: If V is spanned by {v1, v2, . . . , vn} then the flag defined above is called a full flag of V and it clearly has the property that dim Ui/Ui1 = 1 for i = 1, . . . , n