Results 1 to 3 of 3

Math Help - Linearly independence in R3

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    45

    Linearly independence in R3

    Problem:
    Find three vectors in R3 which are linearly dependent, and are such that any two of them are linearly independent.

    What I have so far:
    {v1, v2, v3} is a linearly dependent set.
    {v1, v2} is a linearly independent set.
    {v2, v3} is a linearly independent set.
    {v1, v3} is a linearly independent set.

    a*v1 + b*v2 + c*v3 = 0, where not all a, b, and c = 0 due to linearly dependence.

    If a is not 0 then, v1 = - [ ( b*v2 + c*v3 ) / a ]

    If b is not 0 then, v2 = - [ ( a*v1 + c*v3 ) / b ]

    If c is not 0 then, v3 = - [ ( a*v1 + b*v2 ) / c ]

    And, I am stuck. I don't know what to do after this, much less use this to find three vectors in R3 that satisfy this.

    Thank you in advance,

    -Z
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2010
    From
    Lisbon
    Posts
    51
    What you wrot eis correct, but you're trying too hard. The problem does not require an extensive construction. For example:

    \{(1,0,0),(0,1,0),(1,1,0)\}

    satisfies the required conditions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    45
    Quote Originally Posted by Nyrox View Post
    What you wrot eis correct, but you're trying too hard. The problem does not require an extensive construction. For example:

    \{(1,0,0),(0,1,0),(1,1,0)\}

    satisfies the required conditions.
    Thanks! Lol, I guess I was trying too hard. I just went through the steps to prove that it satisfies those conditions. Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linearly dependent in Q, linearly independent in R
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 12th 2011, 01:44 PM
  2. Span and linearly independence question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 25th 2011, 07:02 AM
  3. Replies: 0
    Last Post: November 15th 2010, 01:24 PM
  4. Linearly independence and dependence of polynomials
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 4th 2010, 07:00 AM
  5. linearly dependent
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 21st 2009, 05:35 AM

Search Tags


/mathhelpforum @mathhelpforum