Please show your work and justify all answers. 1. Consider the system x - y = b1, 2x + 3y = b2, 3x + 2y = b3. What condition (if any) on b is needed to ensure the system is solvable? For find all solutions of the system using elimination and back substitution. Write your answer in the form v = vp + vn, where vp is a particular solution, and the null solution vn is a linear combination of special null solutions. 2. Same question for y + z - 2t = b1, x + y + t = b2, 2y + 2z - 4t = b3, -x + z - 3t = b4. Find the condition on b (if any) so that the system is solvable, and find all solutions in the case b, writing your answer in the same form as in Problem 1. 3. Same question for 2x - y - z = b1, x + 2z = b2 and the choice b.