Find all values a (alpha) for which the resulting system has a) no solution, b) a unique solution c) infinitely many solutions. x - y - az = -1 2x +y + az = -1 -x + y + (a^2 - 2)z = a + 2 attempt: put it in matrix form and row-reduce 1 -1 -a : -1 2 1 a : -1 -1 1 a^2-2 : a+2 after row reducing I get: 1 0 0 : 1 0 1 -2 : 1 0 0 a-2 : 1 so for a = 0 the system has a unique solution (you get x=1; y=0; and z=-1/2) for a = 2 the system has no solution ( you get 0 0 0 : 1 on the bottom row) so I have a values for a unique sol. and no sol. but I still need infinitely many solutions. help. EDIT: if i'm not mistaken really you get a unique solution for any real number, a, that is not 2 (not only 0 as stated above) so how are you supposed to get infinitely many solutions???