Ee1034bS10

Ee1034bS10 - The Basic Idea of Gauss Elimination or...

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The Basic Idea of Gauss Elimination or Pivoting nonsingula ,x, Nnni s i f r 1. , 2. , 3 N has an inverse OR The rows of N are linearly independent OR The columns of N are linearly independent Ax b x 3. , , NAx Nb x EE103 SLIDES 4B (SEJ) 1 Example of Complete Gauss Elimination (CGE) 12 3 1 2 3 1 32 1 4 1 0 0 aaa b e e e x   2 3 622 8 0 1 0 312 9 0 0 1 x x       Ab I 1123 36 3 e g aeee  .. , 123 03 3 x Be e e I  [, , ] 48 9 be e e  3 abasis matrix for R EE103 SLIDES 4B (SEJ) 2
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CGE Pivot (Elementary) Matrices 3 Pivot on a 11 , 1 0 0   1 1 0 0 32 1 622 312   1,1 2 1 0 0 0 1 E -2 1 0 0 0 1 E 12 1 0 0 0 1 0 E 1 1 0 0 0 1 0 E 13 12 11 1 1/3 0 0 2 1 0 E EE E 1,2 -1 0 1 1,2 1 0 1 300 1, 31, 21, -1 0 1 1,3 1/3 0 0 0 1 0 E 1 1,3 3 0 0 0 1 0 001 E EE103 SLIDES 4B (SEJ) 3 0 0 1 0 0 1 CGE 3 1 2 3 1 1 4 1 0 0 aaa b e e e x  3 8 0 1 0 9 0 0 1 Ex x    3 3 aa a b ee e 1 2 12313 43 1300 06 4 1 6 21 0 x x  // / / 3 1 033 5 1 0 1 x Ab E EE103 SLIDES 4B (SEJ) 4
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CGE 123 0 [, , ] B e e e hasbeenreplaced by 11 2 3 1 1 [, , ] B aee 31 2 3 1 2 3 ea e e  12 3 43 3 4 aa e e 16 5 3 ba ee  EE103 SLIDES 4B (SEJ) 5 CGE Fact 3 states: 1 , ] Ba e e 3 1 3 AB A B E A   // 1 06 4 B E A  1 1 1 033 BE I E B    EE103 SLIDES 4B (SEJ) 6
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Ni t 6 a 12313  // CGE 2,2 Now, pivot on 1 -1/9 0 1 06 4 033 A  2,3 2,1 2 0 1/6 0 0 1/2 1 E EE E    12 3 3 aa a b ee e 1 22 43 1300 4 1 6 21 0 5 1 0 1 x Ex x    / / 3 1 11 Ab E  EE103 SLIDES 4B (SEJ) 7 3 1 2 3 a b e e e CGE 1 0 19 49 19 19 0 01 2 3 8 3 1 3 1 6 0 /// / / / 2 1 00 1 1 3 0 1 2 1 / E E 123 1 has been replaced by [, ,] Ba e e 2 [ ,, ] B aae 3 48 13 ba ae  31 2 3 For instance, 93 a e  EE103 SLIDES 4B (SEJ) 8
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CGE As before, Fact 3 states: B aae 2 1 2 3 [, , ] AB A B E E A  22 221 1 21 2 BEE I EE B  EE103 SLIDES 4B (SEJ) 9
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This note was uploaded on 06/01/2010 for the course EE EE 103 taught by Professor Jacobsen during the Spring '09 term at UCLA.

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Ee1034bS10 - The Basic Idea of Gauss Elimination or...

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