# Vectors(linear independence)

1. Apr 10, 2012

### nabzy92

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. Apr 10, 2012

### Robert1986

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).