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## Homework Statement

Given v

_{1}, v

_{2}... v

_{k}and v, let U = span {v

_{1}, v

_{2}... v

_{k}} and W = span {v

_{1}, v

_{2}... v

_{k}, 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 {v

_{1}, v

_{2}... v

_{k}} 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.