1. The problem statement, all variables and given/known data I must describe implicitly the set of the vectors (b_1, b_2, b_3) such that the system has a solution. x-y+2z+w=b_1 2x+2y+z-w=b_2 3x+y+3z=b_3. 2. The attempt at a solution Playing with matrices I got that 0=b_3-b_1-b_2, so that I think that the system has solution for all b_1, b_2 and b_3 such that b_1=b_3-b_2. Am I right? Also, did I describe the set of vectors implicitly? Ah maybe I should write (b_3-b_2, b_2, b_3), for all b_2 and b_3.