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For the following nilpotent matrix A, compute a matrix V R³x³ such that A := V-¹AV is in the Jordan canonical form. Verify by Matlab that your matrix V does as requested. Indicate the dimension of the eigenspace. A = -2 -1

For the following nilpotent matrix A, compute a matrix V R³x³ such that A := V-¹AV is in the Jordan canonical form. Verify by Matlab that your matrix V does as requested. Indicate the dimension of the eigenspace. A = -2 -1

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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For the following nilpotent matrix \( A \), compute a matrix \( V \in \mathbb{R}^{3 \times 3} \) such that \(\Lambda := V^{-1}AV\) is in the Jordan canonical form. Verify by Matlab that your matrix \( V \) does as requested. Indicate the dimension of the eigenspace. \[ A = \begin{pmatrix} -\frac{4}{3} & \frac{2}{3} & -2 \\ -\frac{2}{3} & \frac{1}{3} & -1 \\ \frac{2}{3} & -\frac{1}{3} & 1 \\ \end{pmatrix} \]
Transcribed Image Text:For the following nilpotent matrix \( A \), compute a matrix \( V \in \mathbb{R}^{3 \times 3} \) such that \(\Lambda := V^{-1}AV\) is in the Jordan canonical form. Verify by Matlab that your matrix \( V \) does as requested. Indicate the dimension of the eigenspace. \[ A = \begin{pmatrix} -\frac{4}{3} & \frac{2}{3} & -2 \\ -\frac{2}{3} & \frac{1}{3} & -1 \\ \frac{2}{3} & -\frac{1}{3} & 1 \\ \end{pmatrix} \]
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