Consider the following system of equations: xi + 2x2 + 3x3 = 8 %3D 2^1 + 6x2 + 10хз — 18 x1 + 2x2 + bx3 = a² + 4 2я1 + 5x2 + 823 — 17 x1 + 2x2 + 3x3 = k (a) Find conditions on a, b, k so that this system has a unique solution. (b) Find conditions on a, b, k so that this system has no solutions. (c) Find conditions on a, b, k so that this sytem has infinite solutions.

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