exam1fall2001

Linear Algebra with Applications (3rd Edition)

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mitt 253.1%“ 21001 I FimLNm: .lantName: ' Enn1#1 hflwmhmJMS-cfliy A l. TriturFIhiCflnleTufiTYmm-iflumEpointsfmuchmrmm,udl pointifymdm*lmw.fio Earl-union is "mind. T F The-quinine:[A+H]1=A=+1&B+B‘hnkhfirlflnxnnmfimfi andB. T F Theadmimuffluuquafim 2.1'1+3.z,+4-.2t:,+5.1:I =flfwmalim subapmeut' R‘. T F Ifduumm 55.31111 firmhmm'lyikpandennflmi’mmbc alinearmmhinlflmuffi' and Er. 2 3 U U 0 [I - IhenA [tau-em: . T F H AL 5‘ [0 Bl, mus L) {J I T F ILA-13a 524mlufwimmkifijzd,flmlh¢fmmhmof numxfimmfumahaaianfflnimaguffi. Midlflflzflfl 2 lEmhofli'Ielimrmfannflomiupirmlmrmghemeapmdstnmfiandmly m}uffl1¢uunimdfluwfifl.Mflchtlmn¢No caplanafiunismcdpd. i; m . E 1 1 cm as ' 1 1 was 0.5 3 u ‘E 1‘ 5:10: :fltJ Ell! U] D" 4:3 45] Ella 3‘ I a (1.5- —a. .5 as 2 a 1 _: [1 1| G=l—u5 M H” I13 05] LII: 1] I‘ll I] III]! 3.1.1:: A=E z 4 I I. Findabuiaufllwimmfifmm'infi. A: F: b.17Indahasisufthukmelufmm-ixn. WESLPIU'MI 3 4.End all "mice: Ina-tam with A-l: Yw mm willmminm "binary WWII). 5. Cmsidn' flu: linen syran (5-H! +y -I 6x +{6—rk)y =k whuctiannnm'rm mutant. Fur whinh much] a“: dim thin Ham haw a miqu: mimic“? ‘thn in tlr. mm imam? Unique: auluu'm lf Inmath if Hut]: 253, FIJI 23001 1 Emil 1, Fall 2N1 : Answers Lu. F “Foil”tuseethat {A+B}’=A1+AB+BA+E*.Thisresultisdifferentfi~om s=+2ss+s=,un1essmamccssandsmmmum. 111‘ 'I‘hisisthckemelofmsui: [2 s 4 5] 2 2I' . 1 1 oo23‘#0's' ooss ‘oo' .ir‘= 1 [2 e T Theeolumiisspsnflteitusgesndtheysreindependentsinee rank{A}=42' _.. sw= c. F Considerthe example if: 2 3 cl. T Since matrix is invertible. we have A = 2. tLDis urotation . b. Fisa shear, e. Eisssealittg. d. [F is s pro}ccfion [the column 1Incctot's must be parallel, and there length must not exceed 1}, e. B is s reflection {flie column vectors must be perpendicular unit vectors}. l i} l {l 3. a. 1mm] = span of all four columns =spsn ,H] . Vectors [2] and H form a basis of theimagc. I h.{Noteoveretlyet.) 4 W'te 2 la b a b2 1 Astrsightfonssroe tati sho sthst . n = . u on w s 2 c s c s 3 2 mm _ d b a=dmdc=3b.sothstthesoluuonsareofthcform d],wherebsnddsre arbitrary-constants. . . . . . . 5-1 1 .. . 5. "i‘herelssunique solutioniff the coefficientmstnx A: E. k ts invertible; thisisthecsseiff dens}:(S—klifi—H—o:k‘—llk+24={k—3]{k—B}:cfl. Thus there is sunique solution if i: is neither 3 nor 3. . If it =3 thenthe system takes the form 2.x-I- y =1, ox+3y =3, withinfinitely manysolutions. If k = 8 then file system takes the form —3.t+ y= 1. 63—23: = 3, an inconsistent system. Summary: There is a unique solution if F: is neither 3 nor 8. The system is inconsistent if k = B Hill 253. FIJI. ml 2 . Findingtlukfinslmnnunumfindiugdwmllfiumammgdnmlum. [uska wanduihis “by inspection". in manupficuedcues fimmifim. fl 2—1 {III 012D Ell-l] fl :mmaflmfimmnmmr I: in m: Emu]. NowcmwlmflmnmlumwimammmmLHMnm unli] m'rc. *flmgh“. l 0 D O D l " (I I] 1 "' l 1 I? I) D limtfiévm mm B~i=m=\-El-|él- .- pal-far? ...
View Full Document

This homework help was uploaded on 01/23/2008 for the course MATH 253 taught by Professor Ghitza during the Fall '07 term at Colby.

Page1 / 5

exam1fall2001 - Mitt 253.1%“ 21001 I FimLNm: .lantName: '...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online