First Midterm Exam
MAT 310, Spring 2005
Name:
ID#:
Rec:
problem
1
2
3
4
5
Total
possible
20
20
20
20
20
100
score
Directions:
There are 5 problems on five pages in this exam. Make sure that you have them
all. Do all of your work in this exam booklet, and cross out any work that the grader should
ignore. You may use the backs of pages, but indicate what is where if you expect someone to
look at it.
Books, calculators, extra papers, and discussions with friends are not
permitted.
Feel free to confer with the psychic friends network if you can do so silently.
However, I don’t think Dionne Warwick knows much linear algebra.
1.
(20 points)
Let
V
be the (real) vector space of all functions
f
from
R
into
R
.
a.)
Is
W
=
'
f

f
(
π
2
) =
f
(2)
“
a subspace of
V
? Prove or give a reason why not.
b.)
Is
W
=
'
f

[
f
(
π
)]
2
=
f
(2)
“
a subspace of
V
? Prove or give a reason why not.
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MAT 310, Spring 2005
First Midterm Exam
Page 2
2.
(20 points)
Let
T
be the transformation from
C
3
to
C
3
corresponding to the matrix
1
0
i
0
1
1
i
1
0
a)
What is the rank of
T
? Write a basis for the image of
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 Spring '10
 aa
 Linear Algebra, Vector Space, Dionne Warwick

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