Question: 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

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

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