{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

108AQuiz1

# 108AQuiz1 - id:3 9 Name u 1" Mathematics 108A Quiz 1...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: id :3 9 Name: :- u 1'", Mathematics 108A: Quiz 1 Fliday, Api‘il 9, 2010 I’iofessor J Douglas Meme Part I. TruewFalse~ Ciicie the best enswei to each of the following questions Each question is W01 th 2 points 1. The set Z3 2 {0,1,2}, with the opeiations of addition and u'mltiplicetion modulo thiee is a ﬁeld with ﬁnitely many elements. TRUE? FALSE 2 The set of vectms (123;, mg,e';3,a:4) e R‘l such that 32:; + 252 + 43:3 + 5.7.2; m 3, 3:1 + 2:32 — 5:33 + mi; = 7 is a linear subspace oi R4. TRUE (EALSEU w/ 3. Suppose that V denotes the space of all continuous functions f : R —+ 1R which have a continuous fiist derivatives at every point of 1R, 8. vectoi space over the ﬁeld 1R1 0f reai numbers. Then W = {f E V: f'(.1:) = 3j(ru),for all a: E R}. is e .lillﬁgg';fubspece of V. @l FALSE 4. Let V be the vecto: space of tile precedhig problem Then W a {f E V : f’(m) = 3f(2:)+7,f01a11:c 6 R} is a linear subspace of V, TRUE (FALSE) 5. Let; V be the vectox space of the pieceding pioblems. Then Wm H E V:f’(0) =7} is a lineal subspace of V. eggs) Part II. Give complete proofs 0f each of the following statements 1. a (3 points) Let: W be the set of soiutéons to the homogeneous linear system :13) +232 +353 +515“ 2 0’ 1'1 +2.1”; +2213 +8.14 = 0. :L‘1 +2352 +2353 +8734 W 0' What is the coefficient mam}: of this system? 1215" l '2 I Q, 2 ‘E‘ b (4 points) Use the elementaiy 10w opemsions to put the matrix in low- 1educed (echelon fem}. in,» I, .' 7 w l ’7 Em E: E E .245 z s F 4 .2. .2»? -.| ; , ”a t 325‘ ‘5 .«ﬁ > ) x ‘3 a. 5- “ I?“ i it; P (I; 1 X L. g 1 3 Hr E r " J 5 I ; w n f \ ’ ) ‘ i ‘ I f w. a . r '3' r”? ,f‘ ’x w .‘ i 2. w 1 ! 1 l‘ W; :3“ j (3“ 1 L3.) ' I c (3 points) Note that the solution set W is a lineai subspace of IR“ Find a basis f0] W .. . .~ .. iii: :1: ‘2 2-1:», - '3 “w :bi + 3:. 313?- 4.. .4.) A,“ k") . l a .2 : 1 PS3 + 3 r"? -"z E'- 6"?) R33 :7 9“" a. if] 7»- (“ If? r‘ "5 “ If; :(x‘ALi N31, - r‘ ‘E . 1 r“ 27 p. u“ 2‘ E if M ”" ,2 E 5* l! E E '3 4 - 1 E i " W: 4 i r”: ' ’9 i U ' 3 E % , N . L 2 k, . 3 , g . A. I N '2 n (19?“ f l (“‘3 'E '1 IE \GJQJKQJ ”J“ i O J] 3 ! V .v. o ‘I ~" 2 ' ’ ~ . j r \ > E E .\ w \ 1 ; c : Ant (J i : IO ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern