1. The problem statement, all variables and given/known data Say we have the plane, x+2y+4z=8 (part of a larger problem) 2. Relevant equations 3. The attempt at a solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two vectors. How can this be? We have two linearly independent vectors in a two dimensional vector space that DON'T span it?