erinfreeman6503 erinfreeman6503

16-06-2017
Mathematics

contestada

Find a 2 × 2 nondiagonal matrix whose eigenvalues are 5 and −3, and associated eigenvectors are −1 2 and 1 1 , respectively.

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LammettHash LammettHash

16-06-2017

You're given the diagonal decomposition of the matrix:

[tex]\begin{bmatrix}-1&1\\2&1\end{bmatrix}\begin{bmatrix}5&0\\0&-3\end{bmatrix}\begin{bmatrix}-1&1\\2&1\end{bmatrix}^{-1}[/tex]

Computing the product yields

[tex]-\dfrac13\begin{bmatrix}1&8\\16&7\end{bmatrix}[/tex]

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