- #1
Millacol88
- 86
- 0
Homework Statement
Given v1, v2 ... vk and v, let U = span {v1, v2 ... vk} and W = span {v1, v2 ... vk, v}. Show that either dim W = dim U or dim W = 1 + dim U.
The Attempt at a Solution
I'm not really sure where to start. If I knew that {v1, v2 ... vk} was linearly independent, then it would be easy to prove. But I'm not given anything about linear independence so I'm at a loss.