1. The problem statement, all variables and given/known data What relationship must exist between the constants a, b, and c for the following linear system to be consistent? What is the solution of the system when it is consistent? [tex]x + y + 2z = a[/tex] [tex]2x + 2z = b[/tex] [tex]3x + y + 4z = c[/tex] 3. The attempt at a solution This problem wasn't something we discussed in class so I didn't really have a clear idea of going about it. So I tried to reduce the system to RREF and see what the solutions were in terms of a, b, and c, as shown below: [tex]1......1......2......a[/tex] [tex]0......1......1......(a - b/2)[/tex] [tex]0......2......2......(3a - c)[/tex] Apparently, if I do any further reduction I will eventually get a row with all zeros on the left side, which means the system has no solutions. Obviously, this is not the correct method, because the system must have solutions for their to be any relationship between the constants. Any help on this question is greatly appreciated.