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].