Yes, it should. The basis vectors are in the subspace, so if you have another basis of the subspace, you have to be able to express the vectors in the first basis in terms of the second. If you can't, there's a problem with the bases somewhere, which means you made a mistake somewhere finding them.
By the way, you need a coefficient b on the second vector.
AHHHH sorry I forgot that the coefficients can be fractions. Sorry long night. Thanks for all your help. I think I am going to make one short thread similar to my other one, if you can help out great. If not, you have helped me tremendously. Thanks a lot.