Homework Help

Consider the subset `V = {[[a],[b],[c]] : c=(a+b)/2}` Show that `V` is a subspace of...

user profile pic

hockeyfan54 | Student | (Level 1) Salutatorian

Posted March 25, 2013 at 4:07 AM via web

dislike 0 like

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.

1 Answer | Add Yours

user profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted March 25, 2013 at 4:33 AM (Answer #1)

dislike 1 like

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.`

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes