(i) Use Gaussian elimination and three-digit rounding arithmetic to approximate the
Chapter 7, Problem 5(choose chapter or problem)
(i) 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. 0.03xi + 58.9x2 = 59.2, 5.3Ix, -6.10x2 = 47.0. Actual solution (10, 1)'. 3.3330X, + 15920x2 + 10.333x3 = 7953, 2.2220X, + 16.710x2 + 9.6120x3 = 0.965. -1.5611xi + 5.1792x2 - 1.6855x3 = 2.714. Actual solution (1, 0.5, 1)'. 1.19X| + 2.11X2- lOOxj+X4 = 1.12, 14.2xi - 0.122x2 + 12.2x3 - *4 = 3.44, 100X2 - 99.9X3 +X4 = 2.15, 15.3xi + 0.110x2 13.1x3 ^4 = 4.16. Actual solution (0.17682530,0.01269269, -0.02065405,-1.18260870)'. ex2 + \/2x3 V3X4 = \/11, 7 3 ex2 e x-i + X4 - 0. VSx, V6x2 + X3 V2X4 = JT, Tl^Xy + e 2X2 V7X3 Actual solution (0.78839378, -3.12541367, 0.16759660, 4.55700252)
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