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apm255classnotes_sec4_4

apm255classnotes_sec4_4 - LEE E“ I,m — ‘}é:7:J/yp;ya...

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Unformatted text preview: LEE E“: I ' - ,m — ‘ ,!:%%}é:7(/:J/yp;ya Mfiaé/Jéwgsm ii? ' 7L 4, jam Wm”. 4H4»; H h ff @a 4 1234752 2' fl. E-I M 52, f}; m in Z kfliffi 2/1/ 2.5- 4, fly}? W5 E” “1’ fl *‘fl V“ :23} i I -/‘ ‘ -. M 0/) 71/2727 21sz “WI—{EEZM/ l ‘3? fl-fiéfir‘fi 5* 5 [fix [2:73 flkmfiflm :2 2/ \ I a 4—4»? ! f A 7%.2 Awe-z Wé/w—fik #1115 ‘ 5 | = 7,24 115,11; ”QM 22> g J4; may; ; 7.; x57“ 42, gags i l l. fa K3 II? Z”/ 4, ifs Mpg/W52 ‘. Mm; Zip; .fig fJMF% F l f ' f‘éf?443_li fit/WK A9,, I vizfaééah a g; Mm/‘mzfim Zia/cghgiwt eff ' £236.5— Kufif’Z’:fi ”—2 3.; __ (:9 z? 2:] -—z += as a) 0 c9 c9 4&4}?! :3. W Z Z ”325‘d—2é’“ Instruction: glose books and notes. Show your work and jigsfify your answers Calculators Lpel‘fnittodh 1 (18 rpm ) ldgntfly whether each ofthe foliovfir‘ig matrices is (a) a row-echelon nmuix, (b) ; reducéd row-ochglon matrix (c) an elementary matrix, and (d) invertible Ifa Wis mm= flog! the mverse. (Note tha1(a), (b), (c) and (d) and -éreNOT exclufivec} _ I , f‘ad Y" / (a) yes 1/ :1- 1? 1 72;:0’2 (’2' ;I my; 1/92: mlflOO (ear-OI/ - (611» a: E... 1 EL 2....1 ._ ...Wz/./,/z/¢p ”{3- '7" '1' (i:?(A+B)'=A"+B"',as$um1ngAandBareofthcsamesmefdtmy / . MT We: [ J 3. {10 1:15.) If}! and B are 2x3 maniacs (i.e. the dimensionfsiz: is 2:6), C is a 3x4 _ mmrix and D is a 3x1 matrix, udlich of the following operation is NOT defined? L j . 1 at (i113 +A (um: (iii) DDT (iv) A + c (v) CB 3 W (malaria and (510T (”gyrfixq) (5:4) ((1:3) / 2% 3‘35“?“ W M 55“ flMEJx-AQ =3». {63pm} Given rwo vectors tit and 5 below. (1') draw {he s-‘csuir of «+32, (ii) draw the math (1f—2b. - . _ xl—2x2+x‘=0 .. ‘ 3. {20 pts‘) 302v: the system a and express-2h: solutions) In a vector x: —x2 +x3 +23; :0 form if there: is a solution. ._ a ’"1 a ' "3N2": i -'z of alga. Ea 52. g.” / m.—'=|’) -. J (*{13 Gila —"i GQFZJ fin£| \ th'b 7-”- {éE-HMZ) (“*4/3- z‘réag)m% ‘Q 'g z.— »wgg‘gmfgm) + figmm aw!) =2 2, ' - = 3;};- 5 ' x1 —2-xi ‘h 3‘! _%2 1 {20 pts.) For what values ofk, ifamy, will the 95??ch at 1:; + x3 =__ I; _ : he; _ x _ ' ' gag—x2 +12%“, :23? ' ' solutiomgb} unique solution, amt-(f) 3251?;er ' ' ' ' ' Note: There is only ONE free variable NOT ‘2 free variables" as written above. Please - If discard the last matrix below the check mark and the words below it. ...
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