Results 1 to 4 of 4

Math Help - Prove linearly independent

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    7

    Prove linearly independent

    Prove the statement:

    If u, v, and w are linearly independent, then u+v, v, and w are also linearly independent.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ssl000 View Post
    Prove the statement:

    If u, v, and w are linearly independent, then u+v, v, and w are also linearly independent.
    Given: \alpha \vec{u} + \beta \vec{v} + \gamma \vec{w} = \vec{0} only when \alpha = \beta = \gamma = 0 are equal to zero.

    Now re-write \alpha \vec{u} + \beta \vec{v} + \gamma \vec{w} as \alpha (\vec{u} + \vec{v})+ \delta \vec{v} + \gamma \vec{w} = \vec{0} ....
    Last edited by mr fantastic; December 21st 2008 at 11:01 PM. Reason: Misread the question
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    7
    Quote Originally Posted by mr fantastic View Post
    Given: \alpha \vec{u} + \beta \vec{v} + \gamma \vec{w} = \vec{0} where not all of the \alpha, \beta, \gamma are equal to zero.

    This can be re-written as \alpha (\vec{u} + \vec{v})+ \delta \vec{v} + \gamma \vec{w} = \vec{0} where \delta = \beta - \alpha ....
    Wouldn't that prove that its linearly dependent, since \delta = \beta - \alpha?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ssl000 View Post
    Wouldn't that prove that its linearly dependent, since \delta = \beta - \alpha?
    Sorry I misread the question. I've edited my reply accordingly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linearly independent
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 28th 2011, 12:56 PM
  2. linearly dependent in Q, linearly independent in R
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 12th 2011, 02:44 PM
  3. Prove linearly independent
    Posted in the Advanced Algebra Forum
    Replies: 19
    Last Post: January 26th 2010, 05:25 AM
  4. Linearly Independent
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 23rd 2009, 02:49 PM
  5. Linearly independent set.
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 23rd 2009, 06:12 PM

Search Tags


/mathhelpforum @mathhelpforum