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Math Help - Linear Independence

  1. #1
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    Linear Independence

    Hi,

    I have to questions for everyone,

    if I carry out Gaussian elimination on a matrix of vectors that I am trying to work out if they are linearly independent, if I arrive at a row of zeros, are the vectors always linearly dependent?

    with this set of vectors, I get a column of zeros however the answer says they are linearly independent (1,2,1,3), (2,0,-1,2), (1,1,1,2) (they are transposed)


    Also, in what cases are a set of vectors linearly independent yet do not span Rn? Of course for example if you want to span R3 but only have 2 independent vectors, it is not possible, but are there any other instances?

    Thank You
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  2. #2
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    Smile

    if u have a system of vectors \left \{ V_{1},V_{2}...,V_{n} \right \} that contains the zero vector,this system is dependent.
    Last edited by Raoh; November 30th 2009 at 07:22 AM.
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  3. #3
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    Quote Originally Posted by richmond91 View Post
    Also, in what cases are a set of vectors linearly independent yet do not span Rn? Of course for example if you want to span R3 but only have 2 independent vectors, it is not possible, but are there any other instances?

    Thank You
    if we have n linearly independent vectors, they always span \mathbb{R}^{n}
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