Class 1
1. Write a program for Gauss Seidel algorithm.
2. Use this algorithm as a function and solve 𝑚 simultaneous equations with 𝑛 unknowns (𝑚 < 𝑛) to obtain basic solutions.
3. Check your program for the following examples and find the basic solutions. Consider the non-negativity constraint for all.
a. 2𝑥! + 3𝑥" − 2𝑥# − 7𝑥$ = 1, 𝑥! + 𝑥" + 𝑥# + 3𝑥$ = 6, 𝑥! − 𝑥" + 𝑥# + 5𝑥$ = 4.
b. 2𝑥! + 𝑥" − 𝑥# = 2, 2𝑥! − 𝑥" + 5𝑥# = 6, 4𝑥! + 𝑥" + 𝑥# = 6.
c. 𝑥! − 3𝑥# + 3𝑥$ = 6, 𝑥" − 8𝑥# + 4𝑥$ = 4.
d. 5𝑥! + 4𝑥" + 2𝑥# = .6, 7𝑥! + 2𝑥" + 𝑥# = .35.
e. !" 𝑥! + 2𝑥" + 𝑥# = 24, 𝑥! + 2𝑥" + 4𝑥# = 60.
