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
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35
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j 36 j 37
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j 28 j
j 38 j
"
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39
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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