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Title: Eigenvalues and eigenvectors
Description: Linear algebra course

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C2 Let A

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(approximately) eigenvectors of A
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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
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How are
the corresponding eigenvalues related?

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sum of the entries in each row is the same
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(Hint: See Problem 3
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D4
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Show that v =

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an eigenvector of A
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Title: Eigenvalues and eigenvectors
Description: Linear algebra course