MATH115MF05S

MATH115MF05S - Please Print Id No Faculty of Mathematics...

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Unformatted text preview: Please Print Id. No.: Faculty of Mathematics University of Waterloo MATH 115 MIDTERM EXAM Fall 2D05 Tuesday October 13. 2335 EDI] - 9:133 Mark Instructions: 1. No calculators are permitted. 2. The exam has 9 problems. 3. Make sure to put your own name and ID number at the top of this page. 4. If you do not have enough space to ﬁn— ish your solution to a problem. continue it on the back of the page. and indicate that you have done so. 5. There is 1 blank page at the end of the exam that can be torn off and used for rough work. This exam has 11 pages in total. including the cover and one blank page. ti. CIRCLE YOUR SECTION AND INSTRUCTOR BELUW: Sec. Instructor Time 331 E. Ferguson 8:31] ["32 H. Mggsa___________, * 'Wrgnson 3:30 J [1134 F. Wood 2:33 ["35 P. Wood 3:33 Uilﬁ F. Dunbar 12:33 DDT F. Dunbar 3:343 ["38 W. Kuo 13:33I {"39 W. Kno 3:33 [1113 H. Andre 1:33 MATH I [3] I. Find the ganaral solution to the following : :u- I 40:1 + 32+313 " |1 ]/ SI1+ 32+5-‘B; +- mu The; (Sahara! ﬁniu‘é’“ '5 “5-H MATH 1 ' Page 3 cf:- - {8} 2. Suppuse A, B and (3‘ are all 4 x 4 matrima such _. 2.}: ﬁnd detfﬁ'] = 2. Find [a] det(ABC} z (a m ) -%,l‘(6) Mafia) :m={inr'ﬂfi’7 ‘/ = n -. r (b) dam-103) 0/05 33 = ; 9E5 (13")- 0/595 (0;) i '2 JAKE}; :«CEHHJ r—Q E & 15L) =5 5 (c) detﬂBCT} ﬁﬂﬁliﬂﬁi abﬁs) .- Melt : mﬁ — 3:7) // MATH 1. Midterm {9] 3. {a} Wiite the system in the form ﬁg: = 11 m. F—uu—H—ﬂL—r-ﬁ. f“. ‘5- 1:323?” I if 3 '4 a! Efﬁgy:- rb - I I If U. I + I L 5' ﬂ ‘E’I ﬁt]: it! L..__r—’ 1 1: .— {4'55 1 q " 5 I“_._.___._-—-—'—'_"—-—-—"-"'—————-. '"r ' xi. ".- 1' E I: xj : r g; 5 ,, F, L : 3F 3'; j l p i KI : MATH 1. Midterm . . . l ﬁﬁ-h (b) IsAmvertlble?Expla.u-1. ftibm whgk the Objéfmmht “E {that I‘M! Yﬂt- A If, ﬂﬁﬁ 4th L I \$55M“ *0 0‘ [mt .‘n part5 aythe. ﬁaiéfmment #:0- 1/9 r's {Mara-HF. MATH 1 Midterm %8] 5. Write the matrix A = ( ﬂﬂﬂmﬁrj row upgraiﬁm l 1 2 i 4 as aprodmti: 12a) ﬁlament r-j Mm trim t a a ‘ G G 1."? 1." '3 Ea: U _.i I I} xiii}!!! D a I "I! II‘ t??? h3—'7?§*qt g {Evil '1;- 1 D E] ‘ ﬁr 1: E} 1 ﬂ ‘3! E1(' ‘ If-'r -.-' Lil-“IV a") __ ‘ x -l 0 | ER ’17 " J? "V “U {if T‘- c.- c: _ ,Em Rig-LR; E3: if} _._'|.2_ {J J Eittll i G G i l -1 ﬂ . - Elg Ell-1'13: 2if: {no 1 G CI 0 I J i D ‘3' . R3 :. D I O J; FEE Elﬂ): 3 er: 6- J: “5 " J 1 t :0 g ,. Hi WEIR-Fiﬁ; £6: 0 l _.3_ “216(55qu Flag) 1 Q {.I i“.- £513}: ﬂl _? ﬁ._(§R-} * G I U E1.(E555'E '3' E: E + f\$&55}uéﬁzé*ﬁ:l 'a 0 G '| 4 _I J a 0 a ")( igﬁi'EEJ 4 :Efrrgfrzal a { 1 G _ 'i FF _* _1_r-'1I.F Jl C5 1 D [u- gr£,E;E_:<’-:wfﬁtr”? o C- g;ch- ._-=.. . H orthogonal! X'? = '1 F32: .1313.) and {213* ‘53}- "I I 11 '331‘34] that (Eli-E13m31xq)-Lzaag '533) ID 3x1+3953~513+3\$q U .-|.'_—H - .. . / “HEW {uni-H f'ri f 1 +121 1': IE- [7] 7". Let A = .1“; 1 +12 :33 . Show that ﬂat-{.4} =1+11+n+sli _ 3:1 I: 1 + £3 E + Lil 3"; 2’ 3 1L:- -1_i )!- IL 7:. 3 a :r.‘ 35.; MATH I Midterm Page 9 of 11 N31: [3] 8. Find conditions on (1,1: and c such that the system Ir {'1 551+ Ig+3\$3 = {I E 352 +Ia=b |. 2331+Ig+5\$3=c . f;-r.|r ‘“ ' ‘ {r LﬁIIIU * ist t u: minis Ccnﬁﬂg‘ﬁ'fni If '.t frU-Mr {and n:- 1300115 BE. — ‘ [ I. F E g c 1 .4 t if 1 n "in (1 r {J l i b TERI C, _l —-'. 3.1a 5’" MATHI Midterm Page 100511 Nen‘ “.1... :55...- yea-:9 i [9] 9. Determine if the feﬂwing statements are true or false. Provide I him for yeur ' answer. re" , / f Fe.“ '5 ' If 2:"1-th¥11.‘1isinvertible. x r; if It‘d! 61-1516! LE dadcé) #f 1" W’j I I ‘1 45.33-— ' .. p I: {b} SUPPUEE Ax = in ie an m K n 53; with m < 11. Th the system must have inﬁnitelyr than}; eelutiene. Fa { 35, 35!:3. FEM—11 .——-—— r: ..—_ .3 ...
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MATH115MF05S - Please Print Id No Faculty of Mathematics...

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