1. The problem statement, all variables and given/known data Let A be an m x n matrix with m<n. Prove that the columns of A are linearly dependent. 2. Relevant equations Its obvious that for the columns to be linearly dependent they must form a determinate that is equal to 0, or if one of the column vectors can be represented by a linear combination of the other vectors. 3. The attempt at a solution It seems like there has to be more shown to prove this statement, however this is what I have right now: Let A be an m x n matrix, and let m < n. Then the set of n column vectors of A are in Rm and must be linearly dependent. Is this it? or do I need to state a theorem in here somewhere?