Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions
Hi, i reduced this however i am stuck when it comes to finding the 3 solutions, (infinity, one , no solutions). I am confused with what do they mean with them! would appreciate it if someone can answer what do they mean in general and in this question!
The matrix after reduction:
1 1 0 2
0 1 1 2
0 0 2 2
0 0 (a-b+c) -2a
Question about my solution: Here can we say that z=1
now solving for last row:
(a-b+c)z=-2b -.a-b+c = -2b -> a+c=-b ->b=a+c
a+b+c = 0 ->a+c=-b -> a+c = -(a + c) so 0=0 Thus: infinitely many solutions when a+b+c = 0
and unique solution when a+b+c (not =) 0?