MATH115MF08S_1

MATH115MF08S_1 - Name (Print): W UW Student ID Number:...

Info iconThis preview shows pages 1–9. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name (Print): W UW Student ID Number: University of Waterloo Midterm Examination Math 115 (Linear Algebra for Engineering) Instructor: See table below Date: October 14, 2008 Term: 1089 Number of exam pages: 9 (including cover page) Section: See table below Time: 7:00 p.m. — 9:00 p.m. Duration of exam: 2 hours Exam type: Closed Book Additional material allowed None Circle your instructor’s name and section number Instructor Section Z. Y. Sham 001 S. Wu 002 CD. Roberts 003 R. Andre H y .. E. Martin 006 RY. Roh 007 S. Wu 008 M. Ghandehari 009 R. Malinowski 010 R. Malinowski 011 Instructions 1. Write your name and ID number at the top of this page. Please circle your instructor’s name and your section number up above. 2. Answer the questions in the spaces provided, using the backs of pages for overflow or rough work. 3. Show all your work required to obtain your answers . 4. The use of calculators or any other aids will not be allowed for the test. CHE students GEOE — ENVE students .CIVE students students students) ELE students ME students ME students Mechatronics students Software Eng students MGTE students. Question Mark 1"”? [2] Math 115 Midterm Exam, Fall 2008 Page 2 of 9 Name: 1. Find the (4, 2)th entry of the matrix C. _2 ‘ 0 1 g 2 1 _ f f WA [0 _1 _1] o e, . _1W) r7 i " 5/ (“>- "'45 \.,y/’ “ [4] i2] /,.,/' ' ‘2‘ my} T i h6/Wflj i; E r i G ‘5 i v. 2. Let v = (4,2\/§,—5). (a) Find the unit vector 11 which is in the same direction as the vector v. 197 mu“ where u is the unit vector found in part (a). (b) Compute — /" /., M? l ‘" 47:??? M?- (337140, «.9 m- 3. Compute the midpoint between P(4, Zfi, —5) and Q(1, —4\/§, 3). ------- NEW (IL/1 " : (Li m -e§+ (“a war; ’3‘) 2’. M" (“3“ mi? ~ij Math 115 Midterm Exam, Fall 2008 Page 3 of 9 Name: [4] 4. Solve the matrix equation A — BX : C for X when 1 0 —1 2 —1 0 1 0 ,andC': 0 1 . 0 —1 ~1 1 2 1 2 I?) x“ A: —1—1 ,B: 0 2 J K'\ l5] [3] Math 115 Midterm Exam, Fall 2008 Page 4 of 9 Name: 5. Solve the following system of linear equations. If the solution is not unique express the complete solution as a vector equation. —y+z = 1 2x+y+2z = 0 6. The vector v = (1, b, 1) forms an angle of g with the vector w = (1,0, 1). Find all possible values of b. ' Math 115 Midterm Exam, Fall 2008 Page 5 of 9 Name: [6] 7. Let P(1, —1, 1) be a point in R3 and L be the line a +td where a = (2,1,—2) and d = (2, 0,—1). .A <7 A(a) Find the poi on L which is the closest to P. WWBWWW // (F ( l ’1 (’1 -+ 42+ , “WNW” W 7' \ 7 w: 3 7% 904411615? (Jig-'1‘?me which 3eparm€~z 41%: W?" Math 115 Midterm Exam, Fall 2008 Page 6 of 9 Name: [6] 8. Let P(1, 1,1) and Q(6, 3, 4) be two points in R3. (a) Give a vector equation representing the line passing through P and Q. [6} 9. Give the matrix of the transformation T in each of the following cases: m/ // (a) T : R2 —> R2 is rotation through 7r/ 6. iii: __ , a a re ~ r— » l i 2 CD 3 7% "” 33" fl 7/4 2 ii “in I .L 2 Math 115 Midterm Exam, Fall 2008 Page 7 of 9 Name: [6] 10. Find the value of the following determinants. ,7 \\ 4 1 :1 %’€j\ “é_5‘§~<%21¥<‘§\l3 (a) det 2 2 3 0 0 0 V f 9. "5 4+ , \ '2” ‘ r 5 / 1 l \ a b c (b) det (1+1 b+l c+1 a—l b—l c~1 :3 E C \ I l WW 5"?” 3‘ {rim in i ’1 '4 ’1 MM. I - ‘ (v k“) e, ffo Math 115 Midterm Exam, Fall 2008 Page 8 of 9 Name: [3] 11. Express the matrix A as a product of elementary matrices multiplied by an REEF matrix. 12. Find the scalar equation of the plane through P(2, —-1, 5) that is parallel to the plane 33: — 72 = 5. [3] Math 115 Midterm Exam, Fall 2008 Page 9 of 9 Name: THIS PAGE IS FOR ROUGHWORK ...
View Full Document

Page1 / 9

MATH115MF08S_1 - Name (Print): W UW Student ID Number:...

This preview shows document pages 1 - 9. Sign up to view the full document.

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