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 + 2 = 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.
