# Homework Help: Basic linear algebra proof

1. Mar 3, 2013

### XcKyle93

1. The problem statement, all variables and given/known data
This should be an easy one, I'm just making sure that I'm not screwing up horribly.

Prove that if v is in span(v1,v2, ..., vN), then v, v1, v2, ..., vN are linearly dependent.

2. Relevant equations
span(v1,v2, ..., vN) = {Ʃaivi}.

3. The attempt at a solution
If v is in span(v1,v2, ..., vN), then for some scalars a1, ..., aN, v = Ʃaivi. This means that 0 = Ʃaivi - v, which means that there exists a set of scalars, not all 0, that satisfy the homogeneous equation. This is because the scalar coefficient of v is -1.

Last edited: Mar 3, 2013
2. Mar 3, 2013

### LCKurtz

You mean dependent of course. But your argument is OK.

3. Mar 3, 2013

### XcKyle93

Okay, thanks. I was just making sure!

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