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# MATH 308 D - HW 2 - 2.2 MATH 308

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This 22 page Class Notes was uploaded by BabiiMuffin on Friday October 23, 2015. The Class Notes belongs to MATH 308 at University of Washington taught by Natalie Naehrig in Summer 2015. Since its upload, it has received 93 views. For similar materials see Matrix Algebra in Mathematics (M) at University of Washington.

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Date Created: 10/23/15

Find H II39BE Mariam Um limit are in the span af the given vectmrs 1H 451139 PH 3 ENE V line lif l w Is in the span of the miller green more if so wrilte I as a llmemr cnmblma un at Mlle ULIIBF uecmrs U I cannot be Human as a Illnear enmhlum M the ether me wearers enter DIME In bedI answer Marks 1 39z 4 i1 2 3 32 E 3 II E 3 7 1 7 7 3 7 1 7 i uw gt2 histamine if H is in the spam 0f the Miller gmam mm If m write II as a limanr cumblnaijan at Hills o mr usetnrs IE II canmt be written as in linear mmliiina un Hf u har twn Mumps ertar ME in limit answer blLar ch 1 2 10 i1 1 a2 a b 3 3 m Ila DNE if quot2 Determine if the columns uf u glwm mathc span ml 3 4 The columns spam 3 Tm culumns du mtzmn It 4 Detenmiine if the cullumuis of the given matrix span m3 1 1 6 2 1 53 Tlhe columns span I12 lls eulrumrm dn mt span 1 1 A mamrlx A Is given DamnMilne if the sme A In Where 3 and II hail the approp ataa number elf umpunams has a mlu t nn Mr all choices M II A 4 3 3 5 Q mere Ii 3 soln an of A a b fur every mnlce of Lin Thane it a thiiCE f Iim far A If has m Silurian J A mamrix A is given Detarmine if te system Am 5 lb where n and b have the appmp its numbr on components has a mlul inn araill drains Inf II 7 11 31 2 4 1 2 3 1 11 D 5 There is a salm an aquot A a 1 far ever magic3 9f En Q There is a d wice if b fur which Hi b has m Solution I nd a u u matching dimensilm that Is not in le ghmn spam swungm El H39 nd a v at matclilngl dimension that Is mt in the given spam 9 5 quot H 1 E If a IFind alll valmes of h suth mime vecmrs 111 mg span n1 when a az 113 v 1391 399 Ho39IILinNm 23113112 Find a l values of n such that the vectors in a2 33 span R3 where 44 1 2 a a13 quot 5 2 Dehenniine iii the statement is true or false and justify wur answer If a set of Humor Ind udies I then ii cath spam itquot 0 Time since army linnar annihilation involving time zero vector wllil be the zero vector 039 True sime a net v f metan whim imludes the zero water cam unif spam Hquot391 at must 3 False the zero uecimr can be ind udled wilh any metal vectors which already span It 0 False a m if more cannot span IRquot unless it includes the zero 39veator Deniruling l rf flu stamernenz ls true or false and jus lilfy gmur answer Suppnse A Is a math wll39ljll 1 rows andi m cdlumwns Ill 1 s m I39llhan the cdlurnnns afA spam Itquot 0 True slnca aviary xmlumrm all A must be a nnnzeurn mlnmm 0 True since were are mare columns than ms 1 False since wary Dulun ln of A may be a 2m culurmn 0 False since Illher e are nut enough columns Ian span sf Determlne if the statement ls true or false Suppose A Is a matrix wlth n rows and m columns If m lt n then the columns 0 span Itquot True 0 False Determine if the statement is true or talse and justify yuur answer EA is a matrix mm Calumr spam It then A II has mntrivial sulutimsz False insider A 1 0 Tine Fnrnn s D In hame m mnh iilal solu ansi the columns um cauld ml spam PK 0 True since I its in tin span of u IZDIIJIITIITIE uf A 0 False Camider A 11 Determine if the statement ls true or false If A Is a manIx wlth columns that span Rquot then Ax b has a solution for all h In Rquot 0 True False i Determine if the stamemem Is true or falsei and justify winJr answer If M1 Ila ua spans i3 then so does mm In us uq Q 39Frue the span vi a set ef Vectors can only increase with reswcl to set wmilnmem when adding a wetter In the set 0 True since the Spain of 6mm Ila u m is a submit Iquot the spaun Iquot mm Ila 3 0 False Seminar In u1 0 False Oal ider nu Determine if the statement I true or false and justify ynur answer If M1 ug 3 times not win I13 than naimnar does quot19 llg 3 1ndquot U True since H12 spam of mm Mg as iis a subset of m spam of uh nun M3 14 0 Raise Consider mm 2 l 039 DJ II E E0 1 0 M3 5 D 10 1 and quot1 E 393 D 0 0 True dime the span of 1mmI VIIZ uj quot5 is a autism If the spam of 12mm IIZ uj U Palm Consider may a I a I1 u E 1 I a u a I L to and I14 2 31 1 a Raise Cnnsider mm 2 l1 039 D u 2 UL D CI 39Il3 5 D 1 0 and uq E 0 D 1 Datanulina if the millennium ls true or false and justify vnur answer IF M1 uz ua uh spams R339tl1en so due lll1 uz quot3 U False Consider mm I up IIIf II 1 E III M3 I 1 D and u Ill 1 III 0 True since Hie spam I lm I12 03 liq is a what all l e spam all l m g 113 3933 False Cnmidnr mm E III 0 D u 2 ll 0 a II3 5 D 111 and u E 0 D 1 0 True since the spam 9f lllw Mg uJ lie 3 subsat utf Fllha spam If uh lug 3 I14 0 False Consider mm 1 039 0 II 0 391 393 M3 D 0 11 and u 0 D Q Detenniine if the stamennent is bus or false and justi lr ynur answer If My 2 33 nu nes not span R3 hen neither dines 1131 132 95 0 False Cnnsider39 mm 1 01 01 u It 1 CI M3 D I l and u N D CI 0 False Comldar mm a n a u2 m a a u a m a and quot1 In a 1 m True The span of ml Illa 3 will be a suhsernf the span nf uh um uJ I34 0 True The span of fun Illrz M3 m will be a subset of the span of up ll quot3 U False prraider mm a W I1 II 1 I1 a Mg 39 U E D and 14 1 1w a Detemiiine if the stameniernt is true at false and justify war answer if quot4 Is a quotnear cumbl nadan of uh uh M3 men BPBI39IIII39I quota 3 4 SPBWEIIIL Ila Ila U Falsem sing M4 E spa iulm m 113 I34 but 94 spaHuh m3 0 False Camider in a 1 on a a u a a 1 a a u a a a m a and u E a a um 1 Bi True sin2 liq Is a linear cambina om Bf uh DIE 113 any vector Him span ll um I33 any can be written as a linear mmbina nn af uh 132 mg 0 True Sine uh is a linear combination 91 I111 lllz M3 the any more in npanfuu Illa M3 quot4 are vub uz 3 C False Comlder mm 1 m I 13 ill III II D I u I Iii 111g IZIa and u 1 1 L D Deterrniine if the sh ememt i5 tune or false and justl r yaur answer If 34 is not a linear combina am of um um ugh than all int quot 2 quotB 1 S Spa n h39h quot2 3 Drueu considler u 1 0 D 0 12 Iiir 1 u 01 I133 01 0 L D and B4 ii 1 1 03a False Slings ug is mat a linear combination of full mg mg the ally 39mctnm in spanliul mg M3 11 an M1 lug llj False salute I14 is m a linear cumbinatian of n11I Ma Ma anyI vector m spamuh Ila 3 mm can he wrimm as a linear mmblna un af quot1 um H5 393 True since we spaniul u 3 Ilia but um i spanim up Illa

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