Thread: show columns are linearly independent if homogeneous system has only trivial solution

Let A be an m x n matrix. Show that the columns of A are linearly independent iff the homogeneous system Ax=0 has just the trivial solution.

I think I need to use the fact that a homogeneous system of n linear equations in n unknowns has a nontrivial solution iff rank(A) < n

You only need to express the system in the form and apply the definitions of linearly independence and solution of a system.