hw2 - H? and I'IUJ'I- I 2 J I 2 3 {c} I I 2 {III I I 2 I1 I...

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Unformatted text preview: H? and I'IUJ'I- I 2 J I 2 3 {c} I I 2 {III I I 2 I1 I 2 J 3 4 13. Invert each ofTh-e falluwing maniacs. I'r' p-I'Mihlt‘.‘ ; ‘1 fl _I | 2 {:0 ‘1 {M 4 I} 2 —3 —.'I I —2 _l 2 2 J —2 5 5 I 1 3 1 I 3 It] I | 2 Id} [II I E I 1 III | U 3 l1. Find me inverse. If it en's-ts. [breach {If 1hr; following: I I I | I 1 2 | 1 —I 2 {Hi 2 I 2 [m ' .3; 1 D | —I 2 | ' ‘ I I 3 2 II I : I I I I J. .r 1 In! 1 1 _l l [d]: LII T a .‘i ‘J' I I5 ‘ I 2 2 [2} I 3 I I I 3 U _2 II [I [a] “'1': I 1 I —2 fl 3 1 I I I 5 I 3 3 9 I 1"1’1— —l I I I I 2 n I .I'III Emmi-car; 4'3 arm-1' f4, {NIH-E" Hm! HIM-J ,qh'ew mun-II 2': 1:5' IIMI-r'ngufur and Why {has a pmdmr qfflwnmrmn- IMHHL‘FJ. I’HEIII. Fire-1. Wfil'fi IFIE fur-Era? In :I ffimduc'f I-[Ill-I'II‘HH'FHfl-IT mn- Irfcss; the: LIE-t" Thrumm 2.1,! l 1 I 2 3- 13. ,1 = [ 14. A. = [I I I 2 4 I II 3 . . . l I I5. II A Is a mnmnguinr nLalnI. whose Invent 1}.- 4 2 . find 21. I I I MINA": I I Elfindst IE. “I. III. 11. 2.3 Eleth Writes; Finding A4 125 . Which I'If IhI': fulluwing homogeneous Hystemx have .1 nonlm'iul mlutiII-n'! {HI 2.: .3 = [I {b} 1': + _}'— :={} I: —1}'— "'5:='[} Ax 1-1232“ 11' — 3}.- + 5:: ={} Which HF I'I'u'. I'nIIuwing I'InI'nngcmtflllx syurcmx hurt .‘I nunLn'viaI mlul'mn'! {:1} 3x + '1' + 1.: ={I —x+ _'I'+ :.=il .I-I-E_'I'-I- :24] | I II A: I H H | 2 a flit-IRE. ‘I‘I’Iuil. is 31' "5‘ Fur wth walnut. urn Ila-:5: II'IL' hun'I-Irgenutmu 53:5;an [u — I:I_I.' + 2: + {IT — |]_I.'=fl' 2y=III have Ii FIUI'Jlri'Ir'itIJ sululifln'.‘ A: 3] 1'5 nunsingular 'II' and Illnlz.r il'ud —hr' % I}. II IIIih L'nIIIJiLI'un hold?“ mow Ihal From: that {I —I3 and — be —r a rnI' — hr .I I rm' — hr :1. _ = rm' — hr er places. ICI'tI‘ COII'I- we. that. if .I‘lfi. such 1"“. ’_.r— Ii I 3. II. Dclemline whether I 4 1 . 2 3 II Ii, _ I L I i I —I II 3 la a linearly indepmdent set in 5.“. Determine whether II=Il3 I 2H3 EI—Sj.l—3 I. —II]| i321 linearly independent set in R3. I'II Eren'isea' 5 rhmugh ti. It'd-Ht ,IEI'I'I'II augmented InrrrI'IJr III (III- II'I'eIr‘jirmI EIIIIIII'I'IHI I I ,I. 5. ill. ll. 3 I 4 I I II I 2 3 I E II I I 2 II E II I I 1 I E II III the Set .'I' linearl} independent." I II —3 II I II II I 4 II E II II II II I E II II II II II E II III the net .‘i‘ linearly independe nl'.’ I 2—3!“ tl—I IIEII II II 3::3 [A E 0]. where. A iI-I 5 2!". 5 and nquaingIIlar. IS the 51.215 li:IIIEarl3r iIIIIe:plenrle'nt'II «=1 —4 —4 Latin: —| .'|l'3= [I 'll' I I re the solution apnee nt' II = II. III In. 1;. x1] lint-art}- independent? III Iiie set .‘I' linearly independent? .IIt; = —1 heinng I I 1 II Len“ : II ’3“: I I I II null spare III' A. III III. . 13. 1.1.} linearly independent? l n I III = ,1 twining In: 1h: Wliieh III the given 1reetrIn-I in R1 are linearly.r dependent? FIIr thIIIIe which are. expreaa IIne veeIII-r III-I Ii linear EI‘IITI— binntiun III" Il'll.‘ rLIILI In [2 —I [I].[t] 3 2 [hi [I I II]_[3 It I] Let [I I IIj.[II 2 I ll. I3. I4. l5. In. 1?. 13. III. 4.5 Linear Independence 22'! Cenaiderthe I«elutur apnee M33. Full-aw the direeliuns Irl' Exercise 1 l. I; :III 2H3.“ II: ::I I: III: III II I: Ill? :I-I: ill? I] CenIiIIer lhe Ireel-In rip-nee .II-‘g. FUIIIIw lhe direelium of Exercise l I. IaI :1 + LI IrI II':+I+I.3I1-l-I- 3.: -I I3 Ler I." III: Ihe beetnr IIrIaee nl' all real-valued enntinunux t'urIetiIInII. FIIIII'III' the elirIIeII'nnI: rII Exereiye | I. 2.: |-I Iln 2H+I.I’+J.I {al em I'. IIin I, I“ [h]. .I" f" 5].” {e} r".r.e’ {III LYJGII.‘illIJI‘.Etfi3I Cnnaider the 1reelnnr Hpaee R'i'. F'nllriw Ille directi-IIIIII III' erreifie l l. I It I taI II I .1 [I I —l 1 [l l 2 till —2 . “I l l —.’I l I —2 I 2 —I tell II I. 2 II I I II —l ]. r: in H1 lineaI'lI.I dependent? FIJIF what 1IIaILIeII III I' are the veernr'I [—I [2 | 1].:Inrlll l FIIr what 'IIIII aeII III" I' are the III-mm” +3 and '2! -l- I‘2 -l- 2 in P, linearly independent? Let a and v be nonzero veelerI-I in II VtL‘I'lfl-I'HPIIL‘L‘ 1-“. Shnw thnl u and 1r are linearly dependent il'and Han if there iII II IIealar I- seek than 'I-' _ IIIu. Eeluivrrlently. a and v are linearly independent I'l' and unly il' IIeiIlIer veeIIIr 15 II IIIIIIIiplI: III the tuner. Let .‘i' : Em. r3. ....1'II he a set III vectors in a 1IIIJI'tnr Hpnee V. PrrwIe that S in linearly delaend-ETIL if and Ullll'y' if am.- at the I-eeIurII in .‘II' iII a linear enmbinatien of all the ether remrrnm in .5'. Supreme that .‘IC = l'I'..'.I_I.1rII II. a linearly.I indepen- dent wel nl' veelnn‘. III a reelnr npaee l". Prove that i" = In..w~.w~.l i3 .lllhl'l linearly independent. where w. — r. + 'I': + h. w: = 'l-'_-+ III. :llItl'I't'I : In. ...
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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hw2 - H? and I'IUJ'I- I 2 J I 2 3 {c} I I 2 {III I I 2 I1 I...

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