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Gaussian Elimination

Gaussian Elimination. Major: All Engineering Majors Author(s): Autar Kaw http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Naïve Gaussian Elimination. A method to solve simultaneous linear equations of the form [A][X]=[C]. Two steps

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Gaussian Elimination

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  1. Gaussian Elimination Major: All Engineering Majors Author(s): Autar Kaw http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates

  2. Naïve Gaussian Elimination A method to solve simultaneous linear equations of the form [A][X]=[C] Two steps 1. Forward Elimination 2. Back Substitution

  3. Forward Elimination The goal of forward elimination is to transform the coefficient matrix into an upper triangular matrix

  4. Forward Elimination A set of n equations and n unknowns . . . . . . (n-1) steps of forward elimination

  5. Forward Elimination Step 1 For Equation 2, divide Equation 1 by and multiply by .

  6. Forward Elimination Subtract the result from Equation 2. − _________________________________________________ or

  7. Forward Elimination Repeat this procedure for the remaining equations to reduce the set of equations as . . . . . . . . . End of Step 1

  8. Forward Elimination Step 2 Repeat the same procedure for the 3rd term of Equation 3. . . . . . . End of Step 2

  9. Forward Elimination At the end of (n-1) Forward Elimination steps, the system of equations will look like . . . . . . End of Step (n-1)

  10. Matrix Form at End of Forward Elimination

  11. Back Substitution Solve each equation starting from the last equation Example of a system of 3 equations

  12. Back Substitution Starting Eqns . . . . . .

  13. Back Substitution Start with the last equation because it has only one unknown

  14. Back Substitution

  15. THE END http://numericalmethods.eng.usf.edu

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