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Math 20F  Linear Algebra  Spring 2003
Answers for Selfassessment Quiz #6.5 — June 5
1.
Let
A
be the matrix
A
=
111
022
005
.
Answer the following questions: What are the eigenvalues of
A
?F
o
r
each eigenvalue, what is the the dimension of its eigenspace?
Is
A
diagonalizable? Is
A
defective?
ANSWER: These questions can be answered without having to do any
hard calculations. Since
A
is triangular, its eigenvalues are the diagonal
entries,
λ
1
=1
,
λ
2
=2
,
λ
3
=5
. Since the eigenvalues are distinct, each
eigenspace has dimension 1,
A
is diagonalizable and
A
is not defective.
2.
Now let
A
=
020

305
. Find all of
A
’s eigenvalues and eigenvectors.
ANSWER: To ﬁnd the eigenvalues, we have
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This note was uploaded on 04/23/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.
 Spring '03
 BUSS
 Linear Algebra, Algebra

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