This seems like a very simple problem, yet I can't seem to come up with the correct solution. Determine all the values of c for which the system has nontrivial solutions, and then find all the solutions. x + 2y + cz = 0 3x - y = 0 -2x + y + z = 0 OK, the system has nontrivial solutions if the determinant = 0. So I set the determinant = 0 and solve for c. Using cofactor expansion, I have: c(3 + 2) + (-1 - 6) ==> c = 7/5. I plug this into the system and using elementary row operations I still only come up with only the trivial solution x = 0, y = 0, z = 0. I can't go through the steps here. It would be way too tedious, but I've gone over it several times and come up with the same result. What gives? I was promised that if the det = 0 the system has either 0 solutions or infinitely many solutions. Since x,y,z = 0 is a solution there must be infinitely many solutions. Where have I gone wrong? Thanks.