2331_test1_B_key - Lima" Aigebm 233 Tesi I B Page 1 of8 Math 2331 Linear Algebra Test 1 — Vergion B K Last Name w First Name Peoplasoft ID 0

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Unformatted text preview: Lima!" Aigebm 233'} Tesi I - B Page 1 of8 Math 2331 Linear Algebra Test 1 — Vergion B K Last Name w First Name Peoplasoft ID# 0 N0 calculator. 0 No notes or books. 0 Work in the space: provided. Show your work naatly for pogsible partial credit. 0 Box your answers. 1 2 M12 points) Let u 2 O and v: I ; 2 2 $3“ 2 71 5 + 2 , x. a) u v G Tl f ' i {cs 1 K L b)u-v: \wlfogx +2v1 :1: Q» 0) Length ofuz “a”: \/ 322‘. 02‘ + 17'” 5 \1 I; (1) Let 6* be the angle between 21 and v. 005(6) 2 ' ~ “MW 1"+\1~r 11’ : 3 Linear Aigebra 233 1 Tee? I — B 2 MS e) Give a veeter peapendieiilar :9 v: I l a.» f) Give a lineayeembinaiien of u 33d v that equais; w 1a+$vz w“ 2. (10 peims) True or False? .M \ mm if a diagonal matrix does not have any zeros on the diagonal, then it is invembie. M L_ ifbeth AB and BA are defined, then A and 8 mustbe square matrices. E if AB: 8 , then A z I. \ If A is invertible, then Ax : b has a unique Solution for any I) . X:_W if A is a Symmetric matrix, then AA? 2 l . _ a k: __ The inverse Ufa lewer trianguiar matrix is an upper trianguiar matrix. Matrix A i3 3X5, matrix B is 3x5, matrix C is 5X2 and matrix D is 5214‘ True or False? _ F: AC+ AD is defifled. W A__ (A +8)C is defined. l DTC is defined. l The size of CTD is 2x4. Linear Aigebra 2331 Tea: 1 « B Page 3 018 3. (15 pointy} Given the mztriccg below: 1 5 ~2 —4 2 ’ —2 1 g: D: x: o 2 0 —1 2 ~1 ~ \ a W\ O a) 148+Al): “f :2 a i G 1:; A ‘55 2“; C) i .w VM 1» ‘ 3: (All :: A W , i, i I; \C} 0 t3 0 V; m I \ ‘ UH u c) DTx: Wq O ‘ Z: . Linear Mg,ch 233i T33; i — B Page 4 €fo 4. {'20 points) Soive the tbiiewing sysicm by eéiminatia’m and bagii subsiiiuiion. x+4ygz=§5 i q: Wi V ii; 2x+10y+2244 2 is 5; LE 3.x“ + 8}; + 2: Z 39 rflgfixffizalx K LE 4 M 16 2 3 “k ,w312_\+2?9“5)§23 O ~L‘r 5 we W“ W My 1‘3 g11+i1~yé9~3 \ UV 0 @ H 9—1 29.. H :: 12 2:? a: W a :W ‘3? 9*:53‘5 7 Linear Algebé‘a 2331 Test % « B Page 5 OfS 5. ( l 5 points) Given the matrix: “ :L. ’35 E“: 2x 2 I: i: u \q \o :01 Q :: L,— “M 3 M R 9 1 3] b) Factor A into A = LDU (in this version both L and U have 1'8 011 the diagonal and D is a diagonal} matrix.) A: ngwfi‘fm 5W3} 91%} ii” i Linear Algebra 233} 7631 l - B Page 6 GFS 6‘ {110 peinis) Answer the fbiiewing quasiions wit% the given mairices: [U 0 1} 51 0 $11, 5; c“ g; g? Jr {ask P: e 2 0I 2;: I at 2 a! e f L} G QJ 4 O 15 kg i? i_ ? Sefi’f‘fifi («Viki idé a) R 2 02 g {11 1 gig??? 53%;? M3“; 13‘) PA: ? a”; a“ {3: 2:? {LL 7 "M _ x "i C) pl: W C) Q i :P W *2} E, “2:; k i a“; j \ m ’3 d) 13': i x 5:: «:3 g i Linear Aigebra 2331 7. (20 points) TCSi i ~ B Pagé‘: 7 ()f8 21) Find {he inverse 0f the Foliowing matrix using eiiminaiion. } 0 ~11 A: ——; 2 ; 1 4 i \2‘1 4; 22 m1) Q3?“ ‘i {2; lefl +g3'e I?” «w 2mm 9. 3 ‘1 C} C; figfgvfifié {M1 Q h) Solve the equation: , «5 ‘ 2% x 2* @ «era 45:; X W £52, g g {3 w: i ‘3 ‘3 ME a % £7} 2 ":3 1 L;- E {:2 {:3 f C“) w i 1 {'2 :3». {L} f E C} q» % m i <3 i <3 - E 2 <3 {:2 1 w? H“ :1 <2 i : <3 M g‘3 #332? Q :2. *7; Q i “E? ' r ' “M M > 5 g Q a; “Aw? w%>i/a ~4 *9, 4 f; a m V I h A 2 z , w Egg/aw 2/3“ Egg, ’5‘ 2, 9?} 1 0 4 x 0 ~l 2 I y x 2 (Him: This is an equation of the form ASE-:5) 1 4 1 z 0 i “3? ~43 “’~ ., i X “:3 3A 19 m ’~‘““ “3 v: i/Z/ "f g r , , W ~ % N i L: ’k g fix 5 ’3‘ W, i [A 55/ ’1} g M; W2» / 1 if; L, iv 1} L» f“ Linear Aigcbra 233i T635: 1 - B Page 8 03'" 8 Bonus {5 points) If A, B are square matrices of the same 51.20., prove that (518)” : B"A ”'. w: (3513") i5va :5 mggffifi : g: 3: 342% ‘ $11 {awfiim :1 g’imwg : .1 9: r'Ef‘E v: A (iii i; :::’7 gmié (5 points) Let A be a symmetric mgtrix and comider the LDU decomposition of A . I O O I O 0 Iszl I O and I): 0 2 0 ,WhatisA? 0 2 1 O 0 DJ A "2:5 53;?flfi’ééfi‘é‘iw ~53? 3'? 3: EM W“ v; ‘ “(3% W 233%» ...
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This note was uploaded on 02/21/2012 for the course MATH 2331 taught by Professor Staff during the Spring '08 term at University of Houston.

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2331_test1_B_key - Lima" Aigebm 233 Tesi I B Page 1 of8 Math 2331 Linear Algebra Test 1 — Vergion B K Last Name w First Name Peoplasoft ID 0

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