1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear independent

  1. Aug 15, 2010 #1
    1. The problem statement, all variables and given/known data

    If v11,.....,vk,v are linear independent, prove that v[tex]\notin[/tex]


    2. Relevant equations


    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. jcsd
  3. Aug 15, 2010 #2


    User Avatar
    Science Advisor

    I really cannot read what you have here.

    Are you trying to show that "if [itex]\{v_1, v_2, \cdot\cdot\cdot, v_k, v\}[/itex] is linearly independent, then v is not in the span of [itex]\{v_1, v_2, \cdot\cdot\cdot, v_k\}"?

    Since proof by contradiction works nicely, why look for a "direct" proof?
  4. Aug 15, 2010 #3
    i'm just curious, maybe there is a way that i don't know,

    anyway, you wrote

    \{v_1, v_2, \cdot\cdot\cdot, v_k, v\}
    [/itex] is linearly independent"

    is it the same thing as "[itex]
    v_1, v_2, \cdot\cdot\cdot, v_k, v
    [/itex] are linear independent" ??
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook