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Unformatted text preview: ane rotates
into
. That is, each point is an eigenvector of corresponding to eigenvalue
(you
will get the point if you don’t consider this situation) Problem 4.
(a) Setting up 
(b) Setting up 
(c) Setting up  

 gives us:
gives us:
gives us: .
.
. Problem 5.
(a)
Using Matlab/Octave:
eig(A) gives us: 3, 3, 3, 3
Manually:
     ( ) ( )  Simplifying this formula gives us: ( ) ( ) . (b)
For :
[
[ [
[ ] No we can use Matlab/Octave to solve this system using rref:
([
) [ Which means: [ So [ ] [ ] [ ] is the set of base vectors for the eigenspace corresponding to For :
[
[ [ [
[ No we can use Matlab/Octave to solve this system using rref:
([
) [ . Which means: { [ So [ ] is the only base vector for the eigenspace corresponding to . (c) Algebraic multiplicity of 3 is three and algebraic multiplicity of 3 is one.
Geometric multiplicity of 3 is three (since the dimension of corresponding eigenspace is
three) and geometric multiplicity of eigenvalue 3 is one....
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 Fall '13
 KFOURY
 Algorithms

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