I think he proving by contradiction, suppose L.D then get L.I

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- Jan 24th 2010, 11:13 AM450081592
- Jan 24th 2010, 11:24 AMRaoh
- Jan 24th 2010, 02:38 PMBruno J.
One way to prove that $\displaystyle P \longrightarrow Q$ is to show that $\displaystyle - Q \longrightarrow -P$, which is what I did. If $\displaystyle u,v,w$ are linearly dependent then $\displaystyle S$ must be linearly dependent. Thus if $\displaystyle S$ is linearly independent we must necessarily have that $\displaystyle u,v,w$ are also linearly independent.

The proof is given. Which part don't you understand? - Jan 25th 2010, 06:02 AMHallsofIvy
- Jan 26th 2010, 04:25 AMRaoh
if $\displaystyle u,v$ and $\displaystyle w$ were dependent,$\displaystyle \text{dim}_{\mathbb{R}}Span(u,v,w)\leq 2$,therefore $\displaystyle u,v$ and $\displaystyle w$ will be in $\displaystyle Span(u,v,w) $ with a dimension less than 2,hence they can't be independent.

is that what you're trying to say(Thinking)

P.S: i like your proof i just can't see through it.(Headbang)