MAS 801 It's a Discreetly Discrete World Ã¢Â€Â“ Mathematics in Real-life ...

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Lecture 9: 22 October 2008 Example • Find all the eigenvectors of A = 3 1 1 3 • We know the eigenvalues are 2 and 4 • Let’s first try to find the eigenvectors corresponding to eigenvalue 2 • We have to find x such that Ax = 2x 3 1 1 3 x1 x2 = 2x1 2x2 3x1 + x2 x1 + 3x2 = 2x1 2x2 • We get x1 + x2 = 0; if we let x1 = k then x2 = -k • The eigenvectors are given by k , where k ≠ 0 -k
Lecture 9: 22 October 2008 Exercise 6 • Find the eigenvectors of the 3 x 3 matrix B = 0 -1 -1 1 2 1 1 1 2
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Page 3 and 4: Lecture 9: 22 October 2008 Proving
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Page 9 and 10: The Mathematics of Lecture 9: 22 Oc
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Page 13 and 14: How Big is the Web (Graph) Lecture
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MAS 801 It's a Discreetly Discrete World Ã¢Â€Â“ Mathematics in Real-life ...

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