Answer to Question #23199 in Abstract Algebra for Garcia

Question

Following linear system:

(a-1)x + (3a+1)y + 2z = b^2
(a-1)x + (4a-2)y + (a+3)z = -3
2x + (3a+1)y + 3(a-1)z = 2b

a) possible values of a and b so the system has a unique solution.
b) corresponding values of a and b so the system have no solution n infinitely many solutions respectively.