1. The problem statement, all variables and given/known data For which value of k are the vectors linearly dependent? v1=[1,0,1] v2=[1,1,2] v3=[1,2,k] <--Originally written as column vectors 2. Relevant equations 3. The attempt at a solution None of the vectors look like multiples of each other to me...so time to row reduce. Since each vector was written as a column vector, each row should correspond to a different variable. I set up the augmented matrix: 1 1 1 0 1 2 k 0 0 1 2 0 (If I made an error at this point let me know. But since the vectors were originally represented as columns, I figured row 1 from each vector would form column 1 in the augmented matrix.) row reduce: 1 0 -1 0 0 1 2 0 0 0 k-3 0 k=3 would give a row of all zeros at the bottom meaning that we would have a free variable right? Therefore the vectors should be linearly dependent for k=3? I know linear dependence is more formally defined by having a linear equation like c1v1+ c2v2 +c3v3 = 0, where the weights are non-zero, but it's also my understanding that the presence of a free variable indicates linear dependence.