Consider the subset `V = {[[a],[b],[c]] : c=(a+b)/2}` Show that `V` is a subspace of `RR^3` by expressing `V` as the span of a collection of vectors.

Expert Answers
degeneratecircle eNotes educator| Certified Educator

Any element of `V` is of the form``

`[[a],[b],[(a+b)/2]]=a[[1],[0],[1/2]]+b[[0],[1],[1/2]],` for arbitrary `a` and `b.`

Thus, `V` is the span of `[[1],[0],[1/2]],[[0],[1],[1/2]]` and is therefore a two dimensional subspace of `RR^3.`