Class 1
1. Write a program for Gauss Seidel algorithm.
2. Use this algorithm as a function and solve ๐ simultaneous equations with ๐ unknowns (๐ < ๐) 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. 2๐ฅ! + 3๐ฅ" − 2๐ฅ# − 7๐ฅ$ = 1, ๐ฅ! + ๐ฅ" + ๐ฅ# + 3๐ฅ$ = 6, ๐ฅ! − ๐ฅ" + ๐ฅ# + 5๐ฅ$ = 4.
b. 2๐ฅ! + ๐ฅ" − ๐ฅ# = 2, 2๐ฅ! − ๐ฅ" + 5๐ฅ# = 6, 4๐ฅ! + ๐ฅ" + ๐ฅ# = 6.
c. ๐ฅ! − 3๐ฅ# + 3๐ฅ$ = 6, ๐ฅ" − 8๐ฅ# + 4๐ฅ$ = 4.
d. 5๐ฅ! + 4๐ฅ" + 2๐ฅ# = .6, 7๐ฅ! + 2๐ฅ" + ๐ฅ# = .35.
e. !" ๐ฅ! + 2๐ฅ" + ๐ฅ# = 24, ๐ฅ! + 2๐ฅ" + 4๐ฅ# = 60.
