# Checking my answer : For which vectors the system has solution?

1. Jan 20, 2009

### fluidistic

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.