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Gaussian Elimination<br />This method, which is a variation of Gauss elimination method, can solve up to 15 or 20 simultan...
EXAMPLE<br />Resoverthe following system of equations.<br />        3X1  -0.1X2  - 0.2 X 3  = 7.85<br />       0.1X1  +7X2...
     The first line is normalized by dividing by 3 for<br />     The term X1 can be removed from the second row by subtrac...
Then, the second line is normalized by dividing by 7.00333:<br />     Reducing X2 terms in the first and third equation is...
The third line is normalized dividing by 10 010:<br />      Finally, the terms with X3 be reduced in the first and second ...
ADVANTAGES OF THE METHOD OF GAUSS-JORDAN<br />       Note that back substitution is required for the solution.Although the...
BIBLIOGRAPHY<br /><ul><li>http://personal.redestb.es/ztt/tem/t6_matrices.htm
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Gauss

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Transcript of "Gauss"

  1. 1.
  2. 2. Gaussian Elimination<br />This method, which is a variation of Gauss elimination method, can solve up to 15 or 20 simultaneous equations, with 8 or 10 significant digits in the arithmetic of the computer.<br />This procedure differs from the Gaussian method in which when you delete an unknown, is removed from all remaining equations, ie, the preceding equation as well as pivot to follow.<br />Also all the rows are normalized when taken as pivot equation. The end result of such disposal creates an identity matrix instead of a triangular Gauss as it does, so do not use the back substitution.<br />
  3. 3. EXAMPLE<br />Resoverthe following system of equations.<br /> 3X1 -0.1X2 - 0.2 X 3 = 7.85<br /> 0.1X1 +7X2 - 0.3 X 3 = -19.5<br /> 0.3X1 -0.2X2 +10 X 3 = 7.85<br /> First we express the coefficients and the vector of independent terms as an augmented matrix.<br />
  4. 4. The first line is normalized by dividing by 3 for<br /> The term X1 can be removed from the second row by subtracting 0.1 times the first in the second row. In a similar way, subtracting 0.3 times the first in the third line delete the term with the third row X1F2-0.1F1F3-0.3F1<br />
  5. 5. Then, the second line is normalized by dividing by 7.00333:<br /> Reducing X2 terms in the first and third equation is obtained:F1+ 0.033 F2F3+0.0190 F2 <br />
  6. 6. The third line is normalized dividing by 10 010:<br /> Finally, the terms with X3 be reduced in the first and second equation to get:F1+ 0.068 F3F3+0.0425 F2 <br />X1=3<br />X2=-2.499<br />X3=7.001<br />
  7. 7. ADVANTAGES OF THE METHOD OF GAUSS-JORDAN<br /> Note that back substitution is required for the solution.Although the methods of Gauss-Jordan and Gauss elimination can look almost identical, the former requires approximately 50% fewer operations.One of the main reasons for including the Gauss-Jordan, is to provide a direct method for obtaining the inverse matrix.<br />
  8. 8. BIBLIOGRAPHY<br /><ul><li>http://personal.redestb.es/ztt/tem/t6_matrices.htm
  9. 9. http://es.wikipedia.org/wiki/Matriz_(matem%C3%A1tica)
  10. 10. http://www.gaussjordan.edu.mx/metodogj.html
  11. 11. http://docencia.udea.edu.co/GeometriaVectorial/uni2/seccion21.html
  12. 12. http://thales.cica.es/rd/Recursos/rd99/ed99-0289-02/inv02.html</li>
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