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Back to Eigenvalues and Eigenvectors

Exercise 7

Avg difficulty 3.0

For each matrix, find the characteristic polynomial, and the eigenvalues and associated eigenspaces. Also find the algebraic and geometric multiplicities.

  • (a)  (13−4−47)\begin{pmatrix}13&-4\\ -4&7\end{pmatrix}     (b)  (13−3−37−3−66−2)\begin{pmatrix}1&3&-3\\ -3&7&-3\\ -6&6&-2\end{pmatrix}     (c)  (23−302−3001)\begin{pmatrix}2&3&-3\\ 0&2&-3\\ 0&0&1\end{pmatrix}

Hefferon, Linear Algebra, Similarity, Eigenvalues and Eigenvectors, Exercise 7

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.