Use Gaussian elimination and three-digit chopping arithmetic to solve the following linear systems, and compare the approximations to the actual solution.
a. 58.9x1 + 0.03x2 = 59.2,
−6.10x1 + 5.31x2 = 47.0
Actual solution [1, 10]
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].
c. 2.12x1 − 2.12x2 + 51.3x3 + 100x4 = π,
0.333x1 − 0.333x2 − 12.2x3 + 19.7x4 =√2,
6.19x1 + 8.20x2 − 1.00x3 − 2.01x4 = 0,
−5.73x1 + 6.12x2 + x3 − x4 = −1.
Actual solution [0.0998,−0.0683,−0.0363, 0.0465].
d. πx1 +√2x2 − x3 + x4 = 0,
ex1 − x2 + x3 + 2x4 = 1,
x1 + x2 −√3x3 + x4 = 2,
−x1 − x2 + x3 −√5x4 = 3.
Actual solution [1.35,−4.68,−4.03,−1.66].