NC-Lecture-09.pptx - Numerical Analysis Dr Dr Fahad Fahad Ahmad Ahmad LECTURE 09 SOLUTION OF LINEAR SYSTEM OF EQUATIONS AND MATRIX INVERSION

NC-Lecture-09.pptx - Numerical Analysis Dr Dr Fahad Fahad...

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LECTURE 09 Numerical Analysis Dr. Fahad Ahmad Numerical Analysis Dr. Fahad Ahmad
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SOLUTION OF LINEAR SYSTEM OF EQUATIONS AND MATRIX INVERSION
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GAUSS–JORDON ELIMINATION METHOD
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This method is a variation of Gaussian elimination method. In this method, the elements above and below the diagonal are simultaneously made zero
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That is a given system is reduced to an equivalent diagonal form using elementary transformations. Then the solution of the resulting diagonal system is obtained.
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Sometimes, we normalize the pivot row with respect to the pivot element, before elimination. Partial pivoting is also used whenever the pivot element becomes zero .
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Example Solve the system of equations using Gauss- Jordan elimination method: 2 8 2 3 4 20 4 3 2 16 x y z x y z x y z
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In matrix notation, the given system can be written as 1 2 1 8 2 3 4 20 4 3 2 16 x y z    
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(-2) R1 +R2 and (-4) R1+R3 1 2 1 8 0 1 2 4 0 5 2 16 x y z    
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Now, we eliminate y from the first and third rows using the second row. Thus, we get 1 0 5 16 0 1 2 4 0 0 12 36 x y z    
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Before, eliminating z from the first and second row, normalize the third row with respect to the pivot element, we get
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1 0 5 16 0 1 2 4 0 0 1 3 x y z    
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Using the third row of
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  • Spring '19
  • jane smith
  • Howard Staunton, u12, Fahad Ahmad,  l11

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