1. 1 EXERCISES SYSTEMS OF EQUATIONS FOR SEVERAL METHODS BY :DUBAN CASTRO FLOREZ NUMERICS METHODS IN ENGINEERING 2010

2. BALANCE OF MASS 1.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 distilled 2

3. BALANCE OF MASS 3 B WATER =15% ALCOHOL=85% DISTILLATION COLUMN A FOOD 45 lbmol/h WATER =15% ALCOHOL=85% WATER =15% ALCOHOL=85% C

4. 4 Making a general balance to the column the following equations is obtained: 45=B+C 1 Equation 0.2A= 0.85B + 0.03C 2 Equation 0.8A= 0.15B + 0.97C 3 Equation

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

6. 6 3.To solve the following system of equations 2x2 for the graphic method. The solution of the system of equations is

7. 7 4.To solve the following system of equations for the Thomas method.

8. 8

9. 9 d r L

10. 10 x U d

11. 11 5.Aplicar la metodología de Cholesky para descomponer la siguiente matriz simétrica

12. 12 Finally 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-Seidel 13