The definition of a subspace requires 3 things:

1. The zero element is in the subspace.

2. If u and v are in the subspace, then u+v is in the subspace.

3. If v is in the subspace, and c is a scalar, then c*v is in the subspace.

Just consider arbitrary elements of the form u = <u1, u2, u3> (and similarly for v) and see where that gets you.