Consider the following system of linear equations in the variables x, y and z, with parameters a and b:
2x + 5y + az = 2b
x + 3y + 2az = 4b
3x + 8y + 6z = 0
Write down the augmented matrix of this linear system, then use row reduction to determine all values of a and b for which this system has (a) a unique solution, (b) no solution or (c) infinitely many solutions. Justify your answers. Show all work.