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MAS277 Exam Solutions
Spring Semester, 2012-2013
Nick Gurski
1.
(i) bookwork
V is nite-dimensional if it has a nite spanning set. Alternatively, if it has a nite
basis.
(ii) bookwork
The dimension of V is the number of elements in a basis. Every nite-dime
tq-=
hl3
Ar e
rR.
+A
\,u
p
'. rl.-)
8(l
L
+Q LO,
I
h2-
sT
=(A)
tr L V+W
eV
CF
W2-
o)=
tCvti=L
L
tA;C
sw
lr L
-B
A u.a-nt.
30n L' ->
11,"ra zx-i-tts
o
'tAJ
[Ui3 h
CF
I
boala
MAS277
SCHOOL OF MATHEMATICS AND STATISTICS
Vector spaces and Fourier theory
Spring Semester
20122013
2 hours
Attempt all of the questions. Each of the four questions is worth 25 marks, with the
specic allocation shown in brackets.
(i)
Dene what it means