1. The problem statement, all variables and given/known data Determine whether the set of all vectors of the form (sin2t,sintcost,3sin2t) is a subspace of R^3 and if so, find a basis for it. 2. Relevant equations I guess you just need to use the axioms where it is closed under scalar addition and multiplication. 3. The attempt at a solution If I have two vectors u=(1,2,3) and v=(4,5,6) then u+v = (5,7,9). This gives us 5=sin2t, 7=sintcost, and 9=3sin2t. Am I right in saying there's no (real) value of t which will satisfy any of these equations, meaning (sin2t,sintcost,3sin2t) isn't closed under addition and thus not a subspace of R^3?