1. The problem statement, all variables and given/known data Suppose a non-homogeneous system, Ax = b, of 3 linear equations in 5 unknowns (3x5 matrix) and 3 free variables, prove there is no solution for any vector b. 2. Relevant equations Using the rank theroem: n = rank A + dim Nul(A) where n = # of columns; dim Nul(A) = # free variables 3. The attempt at a solution rank A = n - dim Nul(A) = 5-3 = 2 (which represents the pivot columns) How do I know there are no solutions for any vector b knowing there can be at most 3 pivot columns?