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Let (1 1 1 C = 1 1 0 0 1 2 1 1 B = 0 1 1 o o o/ (a) What are the eigenvalues of B? (b) Show that DB = CD (c) Show that B & C are similar. (d) What are the eigenvalues of C? 1 1 0 D = 1 0 1 0 1 1

Let (1 1 1 C = 1 1 0 0 1 2 1 1 B = 0 1 1 o o o/ (a) What are the eigenvalues of B? (b) Show that DB = CD (c) Show that B & C are similar. (d) What are the eigenvalues of C? 1 1 0 D = 1 0 1 0 1 1

Advanced Engineering Mathematics
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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Let \[ B = \begin{pmatrix} 2 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{pmatrix}, \quad C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}, \quad D = \begin{pmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{pmatrix} \] Tasks: (a) What are the eigenvalues of \( B \)? (b) Show that \( DB = CD \). (c) Show that \( B \) and \( C \) are similar. (d) What are the eigenvalues of \( C \)?
Transcribed Image Text:Let \[ B = \begin{pmatrix} 2 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{pmatrix}, \quad C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}, \quad D = \begin{pmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{pmatrix} \] Tasks: (a) What are the eigenvalues of \( B \)? (b) Show that \( DB = CD \). (c) Show that \( B \) and \( C \) are similar. (d) What are the eigenvalues of \( C \)?
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