For each of the following linear systems
(i) Verify compatibility using the Fredholm alternative,
(ii) Find the general solution, and
(iii) Find the solution of minimum Euclidean norm.
(a) 2x - 4y = - 6, - x + 2y = 3
(b) 2x + 3y = - 1, 3x + 7y = 1, - 3x + 2y = 8
(c) 6x - 3y + 9z = 12,2x - y + 3z = 4
(d) x + 3y + 5z = 3, - x + 4y + 9z = 11, 2x + 3y + 4z = 0
(e) x1 - 3x2 + 7x3 = - 8, 2x1 + x2 = 5, 4x1 - 3x2 + 10x3 = - 5, - 2x1 + 2x2 - 6x3 = 4
(f) x - y + 2z + 3w = 5,3x - 3y + 5z + 7w = 13, - 2x + 2y + z + 4w = 0