1. The problem statement, all variables and given/known data "In each of the given cases, decide whether the specified elements of the given vector space V (i) are linearly independent, (ii) span V, and (iii) form a basis. Show all reasoning. V is the space of all infinite sequences (a0, a1, a2, ...) of real numbers v1 = (1,0,1,0,1,0,...), v2 = (0,1,0,1,0,1,...). 2. Relevant equations I know the basic properties of how to row reduce to find linear independence and span, and the fact that an element that has both of these forms a basis. 3. The attempt at a solution The problem is that I don't know how to deal with these infinite sequences. Should I just write them in a matrix and do as I usually do? If I do this, I don't know how to handle the "..." part of either vector. So basically I have no idea how to start the question anyone shed some light?