# Su97Ex2sol - {I St 97 BEN 3412 Exam 2 Name SHDW ALL WORK...

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Unformatted text preview: {I St] 97 BEN 3412!] Exam 2 Name SHDW ALL WORK! Problem 1 (2!) pts) Solve. the falluwing system of equatiuns using the Gauss Jordan Elimination Mcthud. a + h + c + d = I} Ea - i} - c + d = 3 a + 3!: + 2c - 4d = -1 52 + it: r 2-: + d = T WorkArea l 1 l l i} r i r I a Ah 2 -1 —1 1 3 a *3 +3 —r 3 ( LII—,1 3 2 —4 —1 ’5 a 2, , _5 ,, 5 2 —2 1 2' a 4, *1 “1‘ q I I l' l O a: .1 1' g a I l' l f 0 1:: I I 'J'a v: H o , I, I}; —1 ﬂ 9 I I ‘i'a- -I‘ a 2, r -5' -a a a, -f 12}; i J «J r "I: *l 0 *3 —1 Mr 7 '1 o a ‘21 -3 H D a -‘-1 —3 ‘1’ a r r r o I r r l o " f D Q a r l with _l rd 0 I I “1‘3 ..| H ID! I E! «.l' a 0 l *7}; -: a a , mfg _,. no: a ﬁt a J D a a a. a '- 0 0C) a ‘ Cl 2 I a a r r 1:} o G I all a (I) O H O I O 0 r3 I o O r o "" 0 '3' F '3 Ff a, a g 0 J o o r a Su 9’? IEth 342i] Exam 2 Name SHOW ALL WORK! Problem 2 (25 pts} Consider the following system of equations: 1.1 + v + w = 2 2n — v — 3x — 3y = 1 u — 2n + 3w — 3x — 33; = -1 u + w ~ x - 3r = 1 3n + v + 5w - 2x - 23; = 4 A) Show the equations are consistent by transforming the augmented matrix (Mtg) into its Echelon Form by performing a sequence of elert'terttnr}r rotar operations. B) There are 2 arbitrary unknowns. Explain why. C) Without solving for a solution determine if x and 3r are both arbitrary. D) Repeat Part C) for x and w. E] What conclusion can be drawn from the results of Part C} and D}? m 1 1 1 o o 52 r r r u c: 1 2 -1 o —3 -s 51 G F3 -2 -3 +3. 4, 1 -2 a :3 s 1—1 I” j C} -3 a -3‘ W3 “'3 l {l 1 -l -1 .' 1 I G “I a "i ‘J ‘I‘ 1 5 —2 —2 1 Ir 3 -2 ~ 1. r. ~‘L -'L ‘1 Augmented Matrix _ u u it ‘1' _ a I [ C:- t: '1 I .t f D G "2' I‘ i .1 Q r.) '1. c:- l C) I I 1 5. r C, r r t u i a r I r a; H _ - .- _ H .H F i . o *5 a 3 s -?: e u «a c u 0 N o o t d 0 G C} -3, :2, '3 +3 -3 G G _2 O G a o o £1 £1: C: {J #1 1 -1 -'2 dz 9 G "a Q :- CL Q ail C: C: U C} 153 Numb‘ie 3‘1 ﬂrHtk-rarﬁ amtiﬁﬂwﬁ‘i ‘1 5 ‘3 L 1 |.-' 'U 'u-J ' Cr) t 1 1 1'33 t G E5 1"” ‘5' “air hrﬁﬁrmpj ca I a, :l 5’ " I 7": r. o ‘3’ C1 " *i‘i til-Witter) U G nib-t Murat-Halsete 511 9? BEN 342C! Exam 2 Name SHOW ALL WORK! Problem 3 {25 pts) Find the vaIUefs) of K in the system of equations below whieh result in an inﬁnite number of solutions. Use only methﬂds discussed in class. K] + 4x2 + ?x3 = -5 I- x, + x2 + 13 = 1 2x, + 3x; + 4x; = I} X] " I: + K13 = B I H sl-S Is 7 :—s rs 1 :-S 1' I | r t I a --3 —-{p "' G F 1 - I “J l (a vn-I 2 I 1 Z. ‘3- it e: ‘3' ‘5' mm: I up 0 l 2 . ,1, I I ._ {in K" H 4; Li 1, t 5 irks-Lira with ‘5‘ ‘15 lhg‘rxns‘kﬁ thE'if’ ' 2 "2' 53* Earlehﬁn'i. 1% sCi-ET- a O a a I a I ‘3' cs Iii-r3: I a . IL“ - 5 *‘5’ '5' Echaﬁ‘emﬁﬁ leganSﬁ‘t-tnt Chums-1. Su 9’? BEN 34211] Exam 2 Name SHOW ALL WORK! Pmblarn 4 (33 pts} Consider the system of equations A; =1: belnw. 1. Find the inverae of A and the solution L=A"h. 2. Perfﬂrm twa iteratiﬂns of the Gauss—Sada] mathod and cumputa the: true errors in x, y and 1, Le. (El-L, {ET}! and (ET)z at the and Elf the: secnnd iteration. Start with an initialguessnfxﬂ=yﬂ=zﬂ=1. 5x + y + z = 45 x + 53' + z = 25 —x + y + 52 = -55 ‘5' l r r: c.- c: I 5’ I10 1* a l 13' l' C" 1 . riliﬂtuwgit:iegﬁo—1¥-~fl I _ l I -l r 5 1;: a I. .4 l 5': a: a 1 c} {a (9 a r I H:- .r c. _I —I 5' II D f {3. I | o t l :0 ’Lb 'II'L n: c:- r I'ﬂ 'va 'l'b J I q - . a c: Zol ; -I ‘1' o a. w’he ‘z‘m 'Is *lfjﬂ : .5; a I—Irm l'ch "IS : o O .' '.-'5 “+5 : n O .I' G :-J!'LJ I'E'Iél: *lflg "-41 a I a : Jill-a I . a o 1 Hm “I” "5 a a I was arm “I - .d- "' - fl} 1:, g l. '2. *1 -1 “if: (BC-‘3' _ _ _, I be "3 r3 -1 1‘5 E let-'1‘ = 5 4 :2. -s::; 4‘30 U1. *IG 1 '2. at '— q"-5“‘§1 I ‘t‘- 5-l§\$*'1§1 %-—u+ls\$-1?‘t \$u1~1a=gazl ~r~ = q- 5 .- _I. _ = ﬁ‘HS 33' J§'r%a Sﬁls(h%)-_‘§£‘): L (3.13%) 15' %I="‘+J§-?{.'i‘l. ' -H ﬁ-L(”~_§’-_3_l(u __-I‘L37 (vclraqa) S 5 S 3') 115' at =¢|-*‘_‘[ -!:'1: 1 q—L 3.2.. __~__ 41‘5"} = (5'1")? (10.35323! '1 s I h '4 3 3' 1L; .. ,. _ Y) 11: S'Lﬁl n1. '5. = 3-; (5W7j)_l_#(-11373~t3333 (“WIDE 5 Z ='“+“f~ -1_.F‘I. = -1. 1 5TH _a HHS“!- : H5431} 1‘ .3: L 5 1" “"75" {915) "EC-5.11.5 nibLS' (33:89:13 LEzj': |a*('1D.'E¢-3L'} '1 nG.?-E-31 E“. t -- “Iﬁobb-G. ( T31 ‘5 '1 0.093‘1‘1‘ . I 2 ,v‘o ._ (-QRGBW‘LW = -{J_ a? 13.13 ...
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Su97Ex2sol - {I St 97 BEN 3412 Exam 2 Name SHDW ALL WORK...

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