Hi, I came across a question where I needed to prove that a set of vectors are linearly independent. The thing is, I am not sure how to reason the proof properly. Say you have three vectors x1,x2,x3 E R3, and prove that they are linearly independent. Put them into a 3x3 matrix A, row-reduce, if all the columns have leading terms, because there are no non-leading columns, the only solution of Ax=0 is when x=(0,0,0). Thus, x1,x2,x3 are linearly independent. Is this reasoning good enough? I feel like I am missing something. Any help would be appreciated.