Thread: determining whether a subset is subspace

this might be a stupid question,but if V=R^2 and S={(x_1,x_2):2x_1-3x_2=1}, then S is not a subspace of V since (0,0) is not in S, right?

Looks good to me

If both x1 and x2 were zero, that (the zero vector) would not be in S. So you're right. Since zero does not equal one.