1. The document discusses various numerical methods for solving systems of equations, including: Gauss elimination method, graphical method for 2x2 systems, Thomas algorithm, and Cholesky decomposition method. 2. It provides an example problem of mass balance in a distillation column separating alcohol and water. Equations are set up to solve for the quantities of distillate and residue, as well as the percentage of alcohol recovered in the distillate. 3. The document reviews these numerical methods and provides examples of applying each method to solve systems of equations.

1. 1EXERCISES SYSTEMS OF EQUATIONS FOR SEVERAL METHODSBY :DUBAN CASTRO FLOREZNUMERICS METHODS IN ENGINEERING2010

2. BALANCE OF MASS1.In a distillation column it is carried out the process of separation alcohol-water in a food .The alcohol has high purity and the food has in its composition 20%molar ethylic alcohol. If the feeding during the process is of 45 lbmol/h, being obtained a distilled that it contains 85% molar of ethylic alcohol and a residual that it contains 3% molar of ethylic alcohol it calculates: -The quantity of having distilled and obtained residuals -% of food alcohol recovered in the one distilled2

3. BALANCE OF MASS3BWATER =15%ALCOHOL=85%DISTILLATION COLUMNAFOOD 45 lbmol/hWATER =15%ALCOHOL=85%WATER =15%ALCOHOL=85%C

4. 4Making a general balance to the column the followingequations is obtained:45=B+C 1 Equation0.2A= 0.85B + 0.03C 2 Equation0.8A= 0.15B + 0.97C 3 Equation

5. 2.To solve for the method de simple Gauss51/12f1+f212f2-1/6f1 + f36f3-7/71f2+f3

6. 63.To solve the following system of equations 2x2 for the graphic method.The solution of the system of equations is

7. 74.To solve the following system of equations for the Thomas method.

8. 8

9. 9 drL

10. 10xU d

11. 115.Aplicar la metodología de Cholesky para descomponer la siguiente matriz simétrica

12. 12Finally as product of the decomposition it was obtained that:

13. BIBLIOGRAPHY-CHAPRA, Steven C. y CANALE, Raymond P.: Métodos Numéricos para Ingenieros. McGraw Hill 2002.--http://es.wikipedia.org/wiki/M%C3%A9todo_de_Gauss-Seidel13