the new axes.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Let each of the following matrices M describe a deformation of the \((x, y)\) plane. For each given M find: the eigenvalues and eigenvectors of the transformation, the matrix C which diagonalizes M and specifies the rotation to new axes \((x', y')\) along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.
\[
\begin{pmatrix}
2 & -1 \\
-1 & 2
\end{pmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2F5df7a833-3bb0-4445-99fd-647487995921%2F4lh1t4_processed.png&w=3840&q=75)
Transcribed Image Text:Let each of the following matrices M describe a deformation of the \((x, y)\) plane. For each given M find: the eigenvalues and eigenvectors of the transformation, the matrix C which diagonalizes M and specifies the rotation to new axes \((x', y')\) along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.
\[
\begin{pmatrix}
2 & -1 \\
-1 & 2
\end{pmatrix}
\]
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