Show that the system of equations
2x + y + z = -6a
2x + y + (b +1)z = 4
bx + 3y + 2z = 2a
Has a unique solution except when b = 0 and b = 6.
If b = 0, show that there is only one value for a for which a solution exists, and find the general solution in this case.
Discuss the case when b = 6.
Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.