Math 332 – Test 3
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
8
pts
[1]
Complete the definition: Let
A
be any square matrix. A number
λ
is an
eigenvalue of
A
if...
B
8
pts
[1]
Complete the definition: For an innerproduct space
V
, and a subspace
U
of
V
, the
orthogonal
complement
of
U
,
U
⊥
, is...
C
8
pts
[1]
Complete the definition: Let
V
be an inner product space and
h
x
,
y
i
be its inner product. A
norm on
V
is...
D
8
pts
[1]
Complete the definition: Let
X
be a vector space.
X
is the
direct
sum of two subspaces,
U
and
V
, if...
Dr. Emmert Spring 2010
I of IV
Points Earned
of 32
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Math 332 – Test 3
2
18
pts
[4]
Please carefully answer
one
of the following
two
statements
A
Grade
Me
Any set of eigenvectors corresponding to distinct eigenvalues of a matrix is linearly independent.
B
Grade
Me
Every orthogonal set of nonzero vectors in an innerproduct space is linearly independent.
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 Spring '11
 KeithEmmert
 Math, Linear Algebra, 8 pts, Dr. Emmert, 3 2 18 pts, 3 3 18 pts, Dr. Emmert Spring

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