Math 332 – Test 2
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
1
Please answer the following questions.
A
7
pts
[1]
Let
V
be a vector space. Suppose
W
⊆
V
. Carefully deﬁne what it means when we say
W
is a
subspace of
V
.
B
7
pts
[1]
Let
f
:
V
→
W
be a mapping between any two vector spaces and suppose
U
⊆
W
. Deﬁne,
using set builder notation,
f

1
[
U
].
C
7
pts
[1]
Let
V
be a vector space and suppose
B ⊂
V
. Deﬁne what is meant when we say
B
is a basis.
D
7
pts
[1]
State the RankNullity Theorem.
E
7
pts
[1]
Let
f
:
V
→
W
be a mapping between any two vector spaces. Deﬁne what it means when we
say
f
is an isomorphism.
Dr. Emmert Spring 2010
I of IV
Points Earned
of 35
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View Full DocumentMath 332 – Test 2
2
15
pts
[4]
Please carefully answer
one
of the following
two
statements
A
Grade
Me
Let
V
be a vector space. Let
S
=
{
u
1
,
u
2
,...,
u
k
}
be any nonempty subset of
V
. Show that
Span(
S
) is a subspace of
V
.
B
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 Spring '11
 KeithEmmert
 Math, Linear Algebra, Vector Space, Dr. Emmert, Dr. Emmert Spring

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