MATH115MF05P - 501.0170 N3 MATH 115 Tuesday NAME Please...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

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

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 501.0170 N3 MATH 115 . Tuesday October 18, 2005 NAME: Please Print Id. 1%.: Faculty of Mathematics University of Waterloo MIDTERM EXAM Fall 2005 7:00 — 9:00 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 tote], inciuding the cover and one blank page. 6. CIRCLE YOUR SECTION AND INSTRUCTOR BELOW: Sec. Instructor Time 001 B. Ferguson 8:30 002 R. Moose 10:30 003 B. Ferguson 8:30 004 P. Wood 2:30 005 P. Wood 3:30 006 F. Dunbar 12:30 007 F. Dunbar 8:30 008 W. Kuo 10:30 009 W. Kuo 8:30 010 R. Andre 1:30 MATH 115, Midterm Page 2 of 11 ' Name: [8] 1. Find the general solution to the following system 4x1+ $2+8$3 + 2:4 =12 321 + 922+6$3 + 22:4 = 8 w/ 41?] 31612 R; '9 [.2 a" Rtfizf "! I o a A . 3 I c .1 ‘ I O Q -- —9 l ,L/ M/ O I. o 5' ‘9 fiL—JK‘L—bk‘ 9L 91L er. gosh. I ‘f :13 are. (:‘r‘t g £- 13.25 #3:- “// =4 ISL-L: ——‘{ -5’t'r ‘ 0‘1 ‘1'“: '3’ L! ' SI: (‘13-) : (*V-Je z/M-l >4L/ 3-3. S o ’7 t a ) 1., €— ) MATH 115, Midterm Page 3 of 11 Name: [8] 2. Suppose A, B and C are all 4 x 4 matrices such that det(A) = 0,det(B) = —-% and det(C) = 2. Find ta)det(ABC) : 541A méaéE‘ouc = oar/w .// 3-0 I L (b)det(B-102) 3 IL 9M3 : 9‘ = —? :9 '7} (mama?) : M {as 8e) : My? .0410‘ :- Jlié- 9M8 (d) det(ZB)I : 9 V i M 8 I <13 & \ L. 1 fig \\ MATH 115, Midterm Page 4 of 11 Name: [9] 3. (5.} Write the system - _3 3K 2 —[ / A, 4: gum 4,:(3) / In. a ‘3 *. (b)FinclA". -.// Iii—“lice 1.1-! '00 /""/ 0(a) —7 OIO/[IO ’2000/ col-lot 4’ [.10 no: “*7/0l0/1/0fl loo‘fl‘al OO(,_/0/ 0/01/0 o0/-/o/ ,, {'g‘ai / A 5 [)0 via! (c) Use part (b) to solve the system. WA '1 o ’f 3' Page 5 of 11 MATH 115, Midterm 1 2 3 4 1 4 3 a [7] 4.LetA= 12 0 3‘ o 2 0 3 (a) Find det(A). // (b) Is A invertible? Explain. L/fJ .JH’IIca #0 / Name: MATH 115; Midterm Page 6 of 11 Name: 1 2 3 [8] 5. Write the matrix A = ( l 4 3 ) as a product of elementary matrices. 1 2 6 / .9- 3 21"41'193- I 3- 3 I V 3 h—z O .1 o / 3- C I 1 c I 00 Rt"y:.px job _ OJ --— EW 30 E,)’DO 0/ o '1’ 0:0) 0 ° 5’ 01¢ 00.} 06" 0o! Rafi/21.6) I Do 7 0/0 =3: 1’00 00/ _¢:/O/0 0°73. MATH 115, Midterm Page 7 of 11 Name: [6] 5. Two vectors x and y are called orthogonal if x- y = 0. Find all vectors x = (.131, 2:2, 2:3, 3:4) that are orthogonal to both (1,2, —1,2) and (2, 3, —5, 3). “oi-(I/Q—r,1} :. ac, +3.0L-L-9(3+Q.9H1 I // si- (3,3,-s,3) : 0.}, +32% 4x1. 7‘33“? 5° U6. [14“. at, 4-91., -~13+13‘Lr=-° / to}, 4—31.. we‘ll. 1‘3"!” (la-’1/°) ? l_3-—l.lo // MATH 115, Midterm Page 8 of 11 Name: 1+5 $27 553 [7] 7. LetAm ( $1 1+x2 1:3 Show that det(A) =1+I1+$2+I3. $1 $2 1+$3 gig—hi ((a/IJMA apo) - IN», 4-1.. Hi, 31. 7‘; 4M "I"; f”1 +11 IJ-Dl‘. 3.1 (J a “MHz-l is ax In, 7" “4/ : flint, +1.11%) 1 31., at: I lf-Jh at; I UL (Ma : (Ll—.35 #11 +11)/ I 0 a 5kg, atrcaf/ .Bm‘a/z I l o _ g o / 424.6 3-.- ccf/ Freud} MATH 115, Midterm ‘ Page 9 of 11 Name: [8] 8. Find conditions on (1,5 and c such that the system 3:1 + 1122 +3z3 = a :17: +2.73 fl b 2x1 + $2 +5223 = c is consistent. I I 3 an , , 3 .q 0 I I A —) 6, , A .2 I 5 c. o,,_' (“a ——n 4:: 5 xx ° ° 0 44:46 ‘ MATH 115, Midterm Page 10 of 11 Name: [9] 9. Determine if the following statements are true or false. Provide a brief justification for your answer. K/ (e) If A2 = A, then A is invertible. F. u Aw" 44.. AE/l M "AM / a, (b) Suppose Ax = b is on m x 7:. system with m < n. Then‘ the system must have infinitely many solutions. F 17% SUuFM'W‘O 1mm 13."- alum w / (c) Suppose X; and x2 are both solutions to the homogenous system Ax = 0. Then the vector y = 2x1 — 3):: is also a. solution to the homogeneous system. ./ 4,- A33 A (99‘1"31") (I = 9/15; - Man 2 :1. 3 — 3-3“ ;- =4 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern