Repeat Exercise 10 using Gaussian elimination with scaled partial pivoting.

In Exercise 10

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].