Repeat Exercise 9 using Gaussian elimination with partial pivoting. In Exercise 9 a. 0.03x 1 + 58.9x

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Repeat Exercise 9 using Gaussian elimination with partial pivoting.

In Exercise 9

a. 0.03x1 + 58.9x2 = 59.2,

5.31x1 − 6.10x2 = 47.0

Actual solution [10, 1]

b. 3.03x1 − 12.1x2 + 14x3 = −119,

−3.03x1 + 12.1x2 − 7x3 = 120,

6.11x1 − 14.2x2 + 21x3 = −139.

Actual solution [0, 10, 1/7]

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 [0.176, 0.0126,−0.0206,−1.18].

d. πx1 − ex2 +√2x3 −√3x4 =√11,

π2x1 + ex2 − e2x3 + 3/7 x4 = 0,

√5x1 −√6x2 + x3 −√2x4 = π,

π3x1 + e2x2 −√7x3 + 1/9 x4 =√2.

Actual solution [0.788,−3.12, 0.167, 4.55].

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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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