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strojnjashka [21]
3 years ago
7

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

Mathematics
1 answer:
mel-nik [20]3 years ago
5 0
You're given the diagonal decomposition of the matrix:

\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}

Computing the product yields

-\dfrac13\begin{bmatrix}1&8\\16&7\end{bmatrix}
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