(i) First use Gaussian elimination and three-digit rounding arithmetic to approximate
Chapter 7, Problem 7.4.5(choose chapter or problem)
(i) First use Gaussian elimination and three-digit rounding arithmetic to approximate the solutions to the following linear systems. (ii) Then use one iteration of iterative refinement to improve the approximation, and compare the approximations to the actual solutions. a. 0.03x1 + 58.9x2 = 59.2 5.31x1 6.10x2 = 47.0 Actual solution (10, 1)t . b. 3.3330x1 + 15920x2 + 10.333x3 = 7953 2.2220x1 + 16.710x2 + 9.6120x3 = 0.965 1.5611x1 + 5.1792x2 1.6855x3 = 2.714 Actual solution (1, 0.5, 1)t . c. 1.19x1 + 2.11x2 100x3 + x4 = 1.12 14.2x1 0.122x2 + 12.2x3 x4 = 3.44 100x2 99.9x3 + x4 = 2.15 15.3x1 + 0.110x2 13.1x3 x4 = 4.16 Actual solution (0.17682530, 0.01269269, 0.02065405, 1.18260870)t . d. x1 ex2 + 2x3 3x4 = 11 2x1 + ex2 e2 x3 + 3 7 x4 = 0 5x1 6x2 + x3 2x4 = 3x1 + e2 x2 7x3 + 1 9 x4 = 2 Actual solution (0.78839378, 3.12541367, 0.16759660, 4.55700252)t .
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