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?