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1 Q2 key, 2057.3, 12:10-1:30, PDF File Gen. May 12, 2006 Math 2057, Section 3 C. Spring Semester, 2006 D. Quiz 2 kvk is a unit vector. kv=vk is a unit vector. Open book, notes Date of Quiz 1: Jan. 31, 2006 2. Assume v := (3; 4), as in the last problem. A unit vector (there could be more than one) in the same direction as v is Date of Hourly 1: Feb. 7, 2006 Date of Quiz 2: Feb. 23, 2006 232 Lockett, 12:10 PM - 1:30 PM A. (5) B. ( 3=5; 5=4) C. NAME: D. CODE: SEAT NUMBER: Quizzes are open book and notes. Calculators are allowed, but communication with anyone except the instructor through these devices or any other method during an exam is prohibited. Circle your answers on the Quiz 2 sheets. Also put your answers in this table: Quiz 2 Prb. 1 Prb. 2 Prb. 3 Prb. 4 Prb. 5 Ans. Quiz 2 Prb. 1 Prb. 2 Prb. 3 Prb. 4 Prb. 5 Ans. 3. General Remarks This problem and others concern the constrained optimization problem when the objective function is quadratic and the constraint is linear. A simplication is to leave out the cross terms such as x1 x2 in the general expression for the Quadratic objective function. Technically this means that the matrix is diagonalized, which is a gift. This case will be called the diagonalization case. In the diagonalization case, suppose Q and g are Q(x; x) g(x) A. C. No trick questions are intended. Each problem is supposed to have only one correct response. Every eort is made to eliminate errrorrrrs, but the process is far from perfect. Accordingly, if you do not think the correct answer is to be found on the list of options, then write down what you think should be the answer and explain. D. p A. B. v=v; v 6= 0; is a unit vector. YYY v= kvk is a unit vector as long as v 6= 0: (x1 x1 + x2 4x2 ) (1) (2) The gradient of Q is (3; 4; 5) rQ = YYY rg has more than one component. rg = (1; k). 1x1 3x1 + 2x2 + + 4x2 3 4 = 4 = 6 = 7 has seven unknown variables to solve for. CoeÆcient 1 is explicitly shown to emphasise its value. Select the correct response. A. C. 1. Set w := (w1 ; w2 ): Recall that the norm of w is dened to be kwk := w12 + w22 and that a unit vector is a vector of norm 1. Set v := (3; 4): Select the correct response. := 2 2 3x1 + 4x2 4. The system of equations B. Quiz Problems start here. := Select the correct response. B. For multiple choice questions, four possible responses are listed, in some cases on some exams, ve. Select the response that best answers the question and enter your choice on the answer sheet provided. The choice of \none of the above") may be an option. YYY (3=5; 5=4) (3; 4; 5) D. Only one unknown variable has the value 1. YYY No unknown variable has the value 7. Only one unknown variable has the value -1 One unknown variable has the value -2. 5. Suppose 2x1 2x1 2x2 + 2x2 + + Select the correct response. 2 2 = 2 = 2 = 2 2 Q2 key, 2057.3, 12:10-1:30, PDF File Gen. May 12, 2006 A. Q(x; x) g(x) 2 2 2x1 + 2x2 := (2x1 + 2x2 ) 2x1 + 2x2 = 2 := B. Q(x; x) g(x) 2 2x1 + := 2x1 + := C. Q(x; x) g(x) D. := := 2 2x2 (2x1 + 2x2 ) 2x2 = 2 YYY 2 2 2x1 + 2x2 2x1 + 2x2 = ( 2x1 + 2x2 ) 2 None of the above. Seating Chart Please use the seating chart during exams. Seats are numbered according to an alphabetical ordering of class member names. Names and numbers appear below. greenboard " desk 1 5 15 25 35 j 2 j j 6 j 7 j 16 j 17 j 26 j 27 j 36 j 37 j j j 8 j j 18 j j 28 j j 38 j " 9 19 29 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Artigue, Amanda Rebecca Authement, Jason Paul Barner, Christopher Alan Barrington, Bradley Chase Becnel, George Peter Bushong, Gregory Eric Callahan, Kaci Michele Cook, Ross Philip Currault, Daniel Joseph Daniels, Johnny Thomas II Darragh, David Thomas Gee, Kyle Dip Gomez, Thomas Dylan Henley, Joshua Aron Herring, Christopher Bryan Lambert, Fallon Lessley Lomongo, Christopher Lester Long, Benjamin Troy Manor, Bradley David Mansur, Richard Anthony Martinez, Stevie Layne McCann, Joshua Lane Palczynski, Stacy Fay Picou, Amy Leigh Richard, Matthew R Ruiz, Ryan L Schmidt, Megan Faye Shearer, Benjamin David Smirnov, Illya K Swearingin, Lauren Elise Taylor, Brad Keith Vincent, James Paul Voorhies, Alexis Joseph Waguespack, Tony Jude Walsdorf, Ian Scott Wingrove, Shawn Robert Wright, Timothy William Yates, Ryan Andrew Zarei, Sina j j j 3 j 4 j j j 10 j 11 j 12 j 13 j 14 j j 20 j 21 j 22 j 23 j 24 j j 30 j 31 j 32 j 33 j 34 j j j j j j j