1. The augmented matrix for a system of linear equations in the variables x, y and z is given below: [ 1...-1.....1...|..2 ] [ 0....2...a -1.|..4 ] [ -1...3.....1...|..b ] *It's a 3x3 augmented matrix btw. Can't do the big square brackets, so I made do with the smaller ones...* For which values of a and b does the system have: a) no solutions; b) exactly one solution; c) infinitely many solutions? For the values of a and b in c), find all solutions of the system. 2. a) Show that the set of all vectors (x, y, z) such that x + y + z = 0 are subspaces of R^3 (Euclidean space). b) Let u = (2$, -1, -1), v = (-1, 2$, -1) and w = (-1, -1, 2$), i) For what real values of $ do the vectors u, v and w form a linearly dependant set in R^3? ii) For each of these values express one of the vectors as a linear combination of the other two.