# Spanning of vectors

1. Jan 27, 2013

### macca1994

1. The problem statement, all variables and given/known data
Suppose u,v,w are linearly independent, is it true that <u,v,w> does not equal <u,v>

2. Relevant equations

3. The attempt at a solution
I started by defining what it meant to be linearly independent but am unsure where to go from there. I think the statement is true since the span <u,v> won't include any multiple of w but i can't give a solid proof

2. Jan 27, 2013

### micromass

Staff Emeritus
Assume by contradiction that <u,v,w>=<u,v>. Then $w\in <u,v>$. Thus...

3. Jan 27, 2013

### macca1994

oh i think i get it, by assuming that we can say by definition

w=λ1u + λ2v
then there is now a non trivial solution to
λ1u + λ2v + λ3w=0 which contradicts the statement that u,v,w are linearly independent, is that right?

4. Jan 27, 2013

### micromass

Staff Emeritus
That's right!

5. Jan 27, 2013

### macca1994

Sweet, cheers