My homework question is asking me to define the basis of the subspace. S consists of all vectors in the form (x,y,2x,2y) in R4, and the dimension of the subspace.

My book does not do a good job of explaining this so I'm a little lost.

My first guess would be (1, 2, 2, 6) (0, 1 ,0 , 3) and (1, 0, 2, 0). I'm not exactly sure what to do with this or if I'm even on the right track.

Please help!