Results 1 to 5 of 5

Math Help - Linear independence problem

  1. #1
    Junior Member
    Joined
    Dec 2010
    From
    Macedonia
    Posts
    29

    Linear independence problem

    Hello it's me again - need help again :|

    here is the problem:

    Find out if the vectors (2,1,1) (-1,0,1), (1,2,0) and (5,3,0) are linear independent. If they are linear dependent express one of them as linear combination of the rest.

    tnx in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by karagorge View Post
    Hello it's me again - need help again :|

    here is the problem:

    Find out if the vectors (2,1,1) (-1,0,1), (1,2,0) and (5,3,0) are linear independent. If they are linear dependent express one of them as linear combination of the rest.

    tnx in advance
    First since you have 4 vectors in a three dimentional space what does that tell us?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2010
    From
    Macedonia
    Posts
    29
    that they are linear dependent?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by karagorge View Post
    that they are linear dependent?
    Yes if you have more vectors than the dimention of your space they are always linearly dependant

    Now just set up a 3 by 4 matrix with the above vectors as colums and solve for the dependacy constants.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,706
    Thanks
    1637
    Awards
    1
    Can you solve this equation?
    \left[ {\begin{array}{*{20}c}   2 & { - 1} & 1  \\   1 & 0 & 2  \\   1 & 1 & 0  \\ \end{array} } \right]\left[ {\begin{array}{*{20}c}   \alpha   \\   \beta   \\   \gamma   \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c}   5  \\   3  \\   0  \\ \end{array} } \right]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra: Linear Independence question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 3rd 2011, 05:28 AM
  2. Linear Independence
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 4th 2009, 08:49 PM
  3. Linear Independence in linear transformations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 17th 2009, 04:22 PM
  4. Linear independence problem
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 16th 2009, 01:41 PM
  5. Linear Transformations and Linear Independence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2008, 07:36 PM

Search Tags


/mathhelpforum @mathhelpforum