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* Homework #6 Spring 2002 ww fe ECE 2331 — Numerical Methods for Engineers Homework #6 Student Name: Se Toul Student Number: Instructor: Section Number: Proctor: Seat Number: Place all your work in the spaces provided. No credit will be given unless all necessary work is shown. While you may use MatLab or other software to check your answers, you must show detailed steps “by hand.” All calculations should be carried out to four significant digits unless otherwise indicated. Point values are shown in parentheses. 1. (3) Which of the following two systems of equations is more ill-conditioned? : B-\2@ al -3 Axt+y— 3254 3x-y+2z=1 aly 2 -! ke\O LR] aw xeysrces ) axa2y-ze3q, ATV ado | 2.9x-2=8 L7x+3y+2=4 te “4 . Ti3td ABV ~ OTT” 12 18] WAM EE GY Willy Allg = 947 Ke Cicer ousr -atea & hr 6 61 -To = £493 At. = 6.220 sRabl -ARAZ _2L3q ayaa 3° the . ie Le AK IL 41a . NG] ne ie 139. 81 MK Wle= ONG Re a Rowe 2. (9) For the following partially reduced augmented matrix and its scale vector, identify the next pivot element for each of the indicated methods 10 91 34 26 55 14 00 32 57 83 67) _|52 00 4.0 18 19 23 Me ¥ertOr=| 44 0.0 2.7 ~3.6 2.5 42 2.8 a) Gaussian elimination without partial pivoting (“naive” Gaussian elimination). 3.2 b) Gaussian elimination with partial pivoting. 4.0 c) Gaussian elimination with partial pivoting and row scaling. “4.0 8 2d. = .GIS4 ge 130 2 ag 7 1643 =p Pa! 
