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Math Help - Linear dependence/independence

  1. #1
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    Linear dependence/independence

    If it's in r^3, can you still do it if there is 4 vectors but each have x y and z?
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  2. #2
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    Quote Originally Posted by adam_leeds View Post
    If it's in r^3, can you still do it if there is 4 vectors but each have x y and z?
    Do you want to ask whether more than n vectors from \scriptstyle\mathbb{R}^n (here n=3) can be linearly independent? - If so, the answer is no, because a system of n (here 3) homogeneous linear equations in more than n variables (here 4) always has non-trivial solutions.
    Or, in fewer words: 4 vectors from \scriptstyle\mathbb{R}^3 cannot be linearly independent (they are necessarily linearly dependent).
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  3. #3
    A Plied Mathematician
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    because a system of n (here 3) homogeneous linear equations in more than n variables (here 4) always has non-trivial solutions.
    Unless the system is inconsistent.
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  4. #4
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    Quote Originally Posted by Ackbeet View Post
    Unless the system is inconsistent.
    Well, no: a homogeneous linear system cannot be inconsistent, since it always has the trivial solution.
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  5. #5
    A Plied Mathematician
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    True. You did say homogeneous, and I was thinking non-homogeneous.
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