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MAT 1341C Final Exam
April 16, 2004
Duration: 3 hours.
Instructor: Barry Jessup.
Family Name:
First Name:
Student number:
PLEASE READ THESE INSTRUCTIONS CAREFULLY.
1. This exam has 16 pages and you have 3 hours to complete this exam.
2. This is a closed book exam, and no notes of anykind are
allowed. The use of calculators , cell phones, pagers or any
text storage or communication device is not permitted.
3. Read each question carefully you will save yourself time and
unnecessary grief later on.
4. Questions 1 to 10 are multiple choice. These questions are
worth 2 points each and no part marks will be given. Please
record your answers in the space provided on this page.
5.Questions 11 – 15 require a complete solution, and are worth
6 points each, so spend your time accordingly.
6. The correct answer requires justiﬁcation written
legibly and logically: you must convince me that
you know why your solution is correct.
7. You must answer these questions in the space provided.
Use the backs of pages if necessary.
8. Where it is possible to check your work,do so.
9. Good luck! Bonne chance!
1
2
3
4
5
6
7
8
9
10
subtotal
11
12
13
14
15
Total
1
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Let
W
=
{
(
x,y,z,w
)
∈
R
4

xy z w
≥
0
}
. Then,
A. (0
,
0
,
0
,
0)
∈
W
but
W
is not closed under multiplication by scalars
B. (0
,
0
,
0
,
0)
/
∈
W
but
W
is closed under addition
C.
W
is closed under addition but
W
is not closed under multiplication by scalars
D.
W
is closed under addition and
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