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Homework Help: Vectors(linear independence)

  1. Apr 10, 2012 #1
    Q: Is there a set of four vectors in R3, any three of which form a linearly independent set? Prove.

    Okay so i know what linearly independent is, i have 3 vectors which are linearly independent but I can't find a fourth vector to satisfy the need of the questions like:

    vectors: v1 = (0,0,1), v2 = (0,-2,2), v3 = (1,-2,1) these three vectors are linearly independent when you use Guassian Elimination on the matrix:

    | 0 0 1 |
    | 0 -2 -2 |
    | 1 2 1 |

    you get all the scalars equal to 0. So this satisfy the part where "any three of which form a linearly independent set" is written but the first part says need 4 vectors.
    Any suggestions?
     
  2. jcsd
  3. Apr 10, 2012 #2
    Surely come up with a set of three vectors in R3 that form a linearly independent set, right? Now, just add 4th vector that is id to all of them. This is eqivilent to finding a vector that is not parallel to any of the other three.

    For example, if we were to ask for a set of 3 vectors in R2 such that any two of them form a linearly independent set, I would say v1=(1,0) v2=(0,1) and v3=(1,1).
     
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