# If span(S)=span(P), then S=P.

1. Oct 30, 2006

### *best&sweetest*

I have just had linear algebra exam, and one of the questions was to prove or disprove (give a counterexample) that if span(S) = span(P) then S=P.

I gave this example:

S={v} where vector v=(1,2), and P={u} where u= (2,4).
Then, span(S) = span (P) (line through origin parallel to vector (1,2)),
but S does not equal P.

Am I right?
Thank you!

2. Oct 30, 2006

### HallsofIvy

Yes, that's perfectly correct. (And it was kind of a silly question!)

3. Oct 30, 2006

### *best&sweetest*

Thank you! I spent 15 minutes proving that, and then decided to find a counterexample. I was confused because it seemed so easy once I got the idea. Thanks again!