1. The problem statement, all variables and given/known data Find all solutions of a for which the resulting linear system has (a) no solution, (b) a unique solution, (c) infinetly many solutions. x+z=4 2x+y+3z=5 -3x-3y+(a^2-5a)=a-8 2. Relevant equations ...Row reduction 3. The attempt at a solution I solved the augmented matrix and got z=a-5/[(a-2)(a-3)], then got x and y in terms of z. I solved the homogeneous and only got the trivial solution regardless of a's value. I'm thinking that the system has no solution when a=2 or a=3, and has a unique solution when a equals any other real number. Is this correct?