The following matrix A has a double eigenvalue at -2 and a single eigenvalue at -1. Compute its Jordan canonical form, and compute a matrix V such that V-¹AV is in the Jordan canonical form.
The following matrix A has a double eigenvalue at -2 and a single eigenvalue at -1. Compute its Jordan canonical form, and compute a matrix V such that V-¹AV is in the Jordan canonical form.
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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![The following matrix \( A \) has a double eigenvalue at \(-2\) and a single eigenvalue at \(-1\). Compute its Jordan canonical form, and compute a matrix \( V \) such that \( V^{-1}AV \) is in the Jordan canonical form.
\[
A = \begin{pmatrix}
-2 & 1 & -1 \\
0 & -3 & 1 \\
1/3 & -5/3 & 0 \\
\end{pmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19556b7c-c5b6-4b4d-b523-18b6eba0d2d2%2F82fc2e67-a2e6-48de-971d-026d978ea87f%2Fz5vdkaj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following matrix \( A \) has a double eigenvalue at \(-2\) and a single eigenvalue at \(-1\). Compute its Jordan canonical form, and compute a matrix \( V \) such that \( V^{-1}AV \) is in the Jordan canonical form.
\[
A = \begin{pmatrix}
-2 & 1 & -1 \\
0 & -3 & 1 \\
1/3 & -5/3 & 0 \\
\end{pmatrix}
\]
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