MENG 21200 -  Principles of Engineering Analysis II        Problem 1 - Methods to solve sets of linear equations Solve the following system of equations using the indicated methods:   ?1 + 2?2 + 3?3 − 5?4 = −44 2?1 + 5?2 + 4?3 − ?4 = 8 ?1 − ?2 + 10?3 + 2?4 = 44 3?1 − 2?2 + 5?3 − 3?4 = −16 c) The Gauss-Seidel method with relaxation (? = 0

MENG 21200 -  Principles of Engineering Analysis II       

Problem 1 - Methods to solve sets of linear equations

Solve the following system of equations using the indicated methods:

?₁ + 2?₂ + 3?₃ − 5?₄ = −44

2?₁ + 5?₂ + 4?₃ − ?₄ = 8

?₁ − ?₂ + 10?₃ + 2?₄ = 44

3?₁ − 2?₂ + 5?₃ − 3?₄ = −16

c) The Gauss-Seidel method with relaxation (? = 0.95). Plot versus iteration number.

Problem 2 – Comparing numerical methods to solve sets of nonlinear equations 

Solve this system of equations in Jupyter Notebook by implementing the following methods from scratch. 

3?₁?₂ + ?₂ − ?₃ = 12

?₁ − ?²₁?₂ + ?₃ = 12 ?₁ − ?₂ − ?₃ = −2

1. Multi-equation Newton-Raphson method (see Sections 6.6 and 9.6 of C&C).
2. The successive substitution method (see Section 6.1 of C&C).