1. The problem statement, all variables and given/known data Which of the following subsets of R3 are subspaces? The set of all vectors of the form (a,b,c) where a, b, and c are... 2. Relevant equations 1. integers 2. rational numbers 3. The attempt at a solution I think neither are subspaces. IIRC, the scalar just needs to be from R3 and not, for example, an integer for 1 or a rational number for 2. So for number 1, I can multiply the integers of vector (a,b,c) by some non-integer k, ending up with (ka,kb,kc) outside the subset, and thus not a subspace. For number 2, I can multiply the rational numbers of vector (a,b,c) some some irrational number (say, ∏) and end up with (∏a, ∏b, ∏c), all outside the subset and thus not a subspace. Or am I totally wrong?