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Computer Problems
Cl
2
...
70562
1
...
(a)
(b)
(c)
9
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-
-5
-2
-5
-2
-2
2
2
4
4
1
3
2
2
0
2
2
-1
...
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-0
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42918
-0
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34270
[[ ] [ ] [ ]
C2 Let A
1
...
34 ,
0
...
31
2
...
21
...
85
,
and
are
0
...
10
(approximately) eigenvectors of A
...
3
-4
4
4
Conceptual Problems
Dl Suppose that vis an eigenvector of both the matrix
A and the matrix B, with corresponding eigenvalue
D4 (a) Let A be an n x n matrix with rank(A) = r < n
...
,1 for A and corresponding eigenvalueµ for B
...
De
(b) Give an example of a 3 x 3 matrix with
rank(A) = r < n such that the algebraic mul
termine the corresponding eigenvalues
...
in is an eigenvalue of A11• How are the cor
responding eigenvectors related?
(b) Give an example of a 2 x 2 matrix A such that
geometric multiplicity
...
How are
the corresponding eigenvalues related?
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sum of the entries in each row is the same
...
(Hint: See Problem 3
...
D4
...
Show that v =
is
1
an eigenvector of A
...
)