1. The problem statement, all variables and given/known data Determine if vectors <1,-1,0,2,3> <1,0,-1,3,3> <1,-1,0,3,0> <0,1,-1,2,-2> are linearly dependent or independent 2. Relevant equations I have been solving these questions in the book using a matrix and row reducing them. If I wound up with a free variable, I determined the vectors to be linearly dependent. If there was no free variable after row reducing, then I determined the vectors were linearly independent. From the examples in the book, this method worked (unless just by chance?) 3. The attempt at a solution This is the problem that appeared on the first exam. I solved as described, and found a free variable; the answer was marked wrong. I thought the existence of a parameter in a solution set meant that at least two of the vectors were in the same span, therefore linearly dependent. Am I mistaken?