Solve the system 0.0001 ,x_1 + x_2 = 1

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Mathematical Methods for Physics, Ch Root finding, interpolation, numerical linear algebra and quadrature

Problem

Solve the system 0.0001 x1+x2=1,x1+x2=20.0001\,x_1 + x_2 = 1, \qquad x_1 + x_2 = 2 by Gaussian elimination, carrying every intermediate number to three significant figures, as if working on a machine with that precision. ((a)) Eliminate x1x_1 from the second equation using the first equation as the pivot row (no row exchange), rounding each intermediate result to three significant figures, and report the resulting x1x_1, x2x_2. ((b)) Repeat with the two rows exchanged first (partial pivoting), again rounding to three significant figures, and report x1x_1, x2x_2. ((c)) State which result is correct, given that the true solution is x1=1.0001x_1 = 1.0001, x2=0.9999x_2 = 0.9999 to four decimal places.

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