If a, b, and c are distinct numbers, then the following system is inconsistent because the graphs of the equations are parallel planes. Show that the set of all least squares solutions of the system is precisely the plane whose equation is x – 2y + 5z = (a + b + c)/3.

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x - 2y + 5z = a x-2y + 5z = b x - 2y + 5z = C