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# Note for MATH 1313 with Professor Ahmed-Zaid at UH spring roll 2.3

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COURSE
PROF.
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TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15
SQKKNQ 9 0 1 0KI95A Ygltgtul x lq 3941 0 1 O1O zo 00 Iirksg 39gtgt X 3 J 751quot 3 Y 1 391 W W Jiu TAR MR QQ SOMANM q VGF GLJKQ ltL1 S h 11 m 339XD397391v3 ix quot13 5 K l 1K qun xiiT219 T1 J iv g m39 c 3 OR souJU39WS iinLwasz a 5 3L7 Mk T h 7 21 M3351 lnglvxllr39xjkas SDQAJ M sT LT H T v v on rA39Y w 0nquot 0quot X Jim A System of Equations That Has No Solution Example Given the following system x y z 1 3x 7 y 7 z 4 x 5 y 52 7l I Kquot 0 M I t In usmg the GaussJordan elimination method the followmg equivalent matrix was J rW f obtained note this matrix is not in rowreduced form let s see why 1 3 A WM 0 074 74 1 7L L1K 3 QKQl tD tL quot3 kj x r Look at the last row It reads 0x 0y Oz 1 in other words 0 l I This is never true So the system is inconsistent and has no solution Systems with No Solution If there is a row in the augmented matrix containing all zeros to the le of the vertical line and a nonzero entry to the right of the line then the system of equations has no solution T heorem I Ifthe number owlan or equal to the nuMs in a linear system then one of the following is true a The system has no solution b The system has exactly one solution c The system has in nitely many solutions II Ifthere ar has m or it has i a linear system then the system either Section 23 7 Solving Systems of Linear Equations 11 2 L 3 t l IiiQ 391 396 4 L I w e I 1 LL 1 C O Example 2 Solve the system oflmear equatlons usmg t e GaussJordan e Immatlon a method L 1 v 9 LL 3 a I s 2 1 x2yi3z72 CID 1 A O hf 1 3 3 316 7221 I 2xy75z73 13 9 2 I g 3 1 1L 3 9 Q 393 391 Ll 2m L1 434M 3 1quot 111 A Lk k W O L1 Uh o 0 0 O 0 7k i 9f O L l 3 1 L 0 1 9 L M D A mm D 9 O O O O O Vila O 4 QN x O S 7amp5 XiLkEILKMa I it k V096 K 0 1 vau u l KH Ji A 141131 lagL LK2Y Slr 39g 2 1 11 g a sea onzjisomg ViteMLJiea39Eq i 3 1 0 SE 31 1 Example 3 Solve the syi f of linear equations using the GaussJordan elimination method 1 11 l 5 I a i 3 A 53 Q3 1 a F3 is l 39l 3 39 1 k I dLlkl 3 L AL l 3 1 A 393 3 f gt D 3 o l LL 1 i rf L1 l 3 taxiH 0 E S 0 LL 3 l L3 0 R g Li 1 O A q UHlKL o b a 3 M r 07ko r3 mfc lklkk No Suquotiv 05 Section 23 7 Solving Systems of Linear Equations 11 Example 4 Solve the system of linear equations using the GaussJordan elimination method 1 9 9 21 Q 9 x72y 2 1 z 3 7xil4yl4 j 4 Lf G 1 3x76y6 L quot5 Q Mk XL 3 quot 2 LVIU a 9 amp3L quot 5 9 11 7 1 Vs Ml 1 X5 1 F 39m 0N L I i DHQWMSJZV l h V 2 H 1 7 Example 5 Solve the system of linear equations using the GaussJordan elimination J u 7 1 method 39E K O a a K 5 233 a 2 k e K 3 t c xizl o i vawlj39blq LLM l 0 2 JR l 0 3 7 K o 4 O o o D 1C o iiiLOA 140 l 0 him Section 23 7 Solving Systems of Linear Equations 11

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