Solve the following systems of equations using Gaussian Elimination with three-digit rounding arithmetic. Is your answer a reasonable approximation to the exact solution? Compare the accuracy of your answers with the condition number of the coefficient matrix, and discuss the implications of ill-conditioning.
(a) 1000x + 999 v = 1
554x + 555 y = -1
(b) 91x + 175y + 83z = 1
44x + 78y + 37z = 1
52x + 97y + 46z = 1
(c) 3.001x + 2.999y +5z = 1
-x + 1.002y - 2.999z = 2
2.002x + 4y + 2z = 1.002