# Homework Help: Linear independent

1. Aug 15, 2010

### annoymage

1. The problem statement, all variables and given/known data

If v11,.....,vk,v are linear independent, prove that v$$\notin$$

$$\left\langle$$v1,......,vk$$\right\rangle$$

2. Relevant equations

n/a

3. The attempt at a solution

i can prove it by contrapositive, but i'm curious how to proof it with

"If v11,.....,vk,v are linear independent" in the beginning,

any idea? T_T

Last edited: Aug 15, 2010
2. Aug 15, 2010

### HallsofIvy

I really cannot read what you have here.

Are you trying to show that "if $\{v_1, v_2, \cdot\cdot\cdot, v_k, v\}$ is linearly independent, then v is not in the span of $\{v_1, v_2, \cdot\cdot\cdot, v_k\}"? Since proof by contradiction works nicely, why look for a "direct" proof? 3. Aug 15, 2010 ### annoymage i'm just curious, maybe there is a way that i don't know, anyway, you wrote "[itex] \{v_1, v_2, \cdot\cdot\cdot, v_k, v\}$ is linearly independent"

is it the same thing as "$v_1, v_2, \cdot\cdot\cdot, v_k, v$ are linear independent" ??