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Back to Eigenvalues and Eigenvectors

Exercise 12

Avg difficulty 3.0

This matrix has distinct eigenvalues.

(1216−10−1−2−1)\begin{pmatrix}1&2&1\\ 6&-1&0\\ -1&-2&-1\end{pmatrix}

  • Diagonalize it.

  • Find a basis with respect to which this matrix has that diagonal representation.

  • Draw the diagram. Find the matrices PP and P−1P^{-1} to effect the change of basis.

Hefferon, Linear Algebra, Similarity, Eigenvalues and Eigenvectors, Exercise 12

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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.