Hi, i'm having trouble with the following question:
Show that if u,v,w form a basis for a vector space V over the field of scalars K then so do, u+v, u+v+w, v+w.
Any help would be great. Thanks.
now it leaves for us to show that the latter three vectors span the space. since we know u, v and w span the space, we can show this by showing that we can write u, v and w as linear combinations of (u + v + w), (u + v) and (v + w)
Anyway, it is somewhat easy to see that if three vectors are linearly independent and assuming the space as for lack of other indication, they span the space.