MATH115MF05S

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

Info iconThis preview shows pages 1–11. 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

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Page1 / 11

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

This preview shows document pages 1 - 11. Sign up to view the full document.

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