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Class Note for MATH 3321 with Professor Morgan at UH

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This 11 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 58 views.

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Date Created: 02/06/15
Honors Math 3321 Jeff Morgan jmorganmathuh edu http Wwwmathuh eduimorganfNIath3 32 1 T goc WI Qar S 5W Recall as Q 9 7 1 Augmented Matrix migra 7L2quotquot O XCQ I 2 v Iquot I QI7QAQ 17LZFquot QWXAL01 39239 3 U A am397c a XL A Othn lt2m 2 Elementary Row Operatlons m at RKQR 2 disquot DC 0 395 lt3O 32 Question HOW do e 39 a o eementary row operationsA R quot RA k d FO LS1 zRA 7K4 Recall We used elementary row operations to solve 3x10y4z 1 2x7y4252 4x 9yllz15 Solutionzx 1y Oz 1 Example Vlb QN WWN MALer Use elementary row operations to solve amp NO Yn x10y41 cdcujdw 2x7y4z Mg CalCoJOd yr 39 Note A student on class informed me that we entered a number wrong Work through it to get the correct info Row Reduced Echelon Form RREF sfmhl39 1 3quot W T I Vlmivaling Example 9 43 MSW 44 quotI Mquot zg3xz3zrg2 372x4il W39 10 121 EJ 2 1 a 7 1 v o a quot39In quotIn I 2 4 l 4 quot7 o I D In Ills l 9 3 1 If g o I I Q ULmX39 447quot w quot 41 uS 7 hawk 39 9 y a 1 t 39Tgi s a 1 L 33 11 T 1 ix L 114 7 13 1 fr quot1 u 3 1 50 w I39 x 4 1quot 13959 quot 1 B h quot9 4 3 Irvquot WW quot4 umquot u K 0in IW V X can 39039 quotquotS39 The augmented matrix is 2 3 3 1 2 1 2 4 1 1 1 0 3 2 1 R1 ltgt R2 gives 1 2 4 1 1 2 3 3 1 2 1 0 3 2 1 2Rl 1R2 gt R2 gives 1 2 4 l 1 0 7 5 3 4 1 0 3 2 1 1R11R3 gt R3 gives 1 2 4 1 1 0 7 5 3 4 0 2 7 3 0 17R2 gt R2 gives 1 2 4 1 1 0 1 57 37 47 0 2 7 3 0 2R2 1R3 gt R3 gives 1 2 4 1 1 O 1 57 37 47 0 0 397 157 87 I used the Matrix Calculator linked from httponlinemathuhedu 2R2 1R1 gt R1 gives 1 0 187 17 17 0 1 57 37 47 0 0 397 157 87 739R3 gt R3 gives 1 0 187 17 17 0 1 57 37 47 0 0 1 513 839 57R3 1R2 gt R2 gives 1 0 187 17 17 0 1 0 213 2839 0 0 1 513 839 187R3 1R1 gt R1 gives 1 0 0 1113 513 0 1 0 213 2839 0 O 1 513 839 7 ROW Reduced Echelon Form RREF General Process Info E leading wymarow WM 291 0 1 Q CW W5 o we Ev WW 0 W 39 Qo d h Mfr axed M a 0x13 LSEEJA 9V wrp A WPWFM 6 m lh 0 WW60 mm mm W L T 1 3 i l Emma dorm M W MadMC W wg 06 W x a 3 4mm are 0 myef Mow 3 MWS 245 he axMg h OW Cow R 0 W W7 QC m tWWZF WW vrw W 0W Z maJ 0 k Examples Which of the following augmented matrices are in RREF max 40 w aw 0 3RZVA1 9 R H Lj Wm M We Example The RREF of the augmented matrix for the linear system 2541 is Solve the system 1O Quiz 1 1 1 Gnvo the norm of the vectolr 2 1 1 1 1 1 2 W011 If any of the vectors 2 1 and 1 2 3 Write the augmented mum39s associated with 1 are orthogonal x Zyz1 x3y z4 am 7x72y102210 11

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