So in my linear algebra course the following question came up on an exercise sheet:
"Show that determining dependence or independence is equivalent to examining the solution set of homohenous systems, Ax=0. What is the solution set of: i) linearly dependent vectors, ii) linearly independent vectors"
I am genuinely confused by this. I know how to check for dependency using linear combinations, but that is granted I have an actual matrix to work with and not just "Ax". Wouldn't the solution set depend on the vectors of matrix A and entries of x? Is there a set that defines all solutions of all vectors that are linearly dependent or independent?