Find e^(tA). Use e^(tA) = P e^(tD) P^(-1). The matrix is \begin{pmatrix}1&2&0\\ 0&1&-2\\ 2&2&-1\end{pmatrix}. Use det(A-λI) for eigen values and the find eigen vector using Av = λv. For the eigen vector : \begin{pmatrix}1&2&0\\ 0&1&-2\\ 2&2&-1\end{pmatrix}\cdot \begin{pmatrix}x\\ y\\ z\end{pmatrix}=λ\cdot \begin{pmatrix}x\\ y\\ z\end{pmatrix}. After finding the eigen values, use this to find eigen vectors. Then find e^(tA). use e^(tA) = P e^(tD) P^(-1).

Find e^(tA). Use e^(tA) = P e^(tD) P^(-1). The matrix is \begin{pmatrix}1&2&0\\ 0&1&-2\\ 2&2&-1\end{pmatrix}. Use det(A-λI) for eigen values and the find eigen vector using Av = λv. For the eigen vector : \begin{pmatrix}1&2&0\\ 0&1&-2\\ 2&2&-1\end{pmatrix}\cdot \begin{pmatrix}x\\ y\\ z\end{pmatrix}=λ\cdot \begin{pmatrix}x\\ y\\ z\end{pmatrix}. After finding the eigen values, use this to find eigen vectors. Then find e^(tA). use e^(tA) = P e^(tD) P^(-1).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 66E: Show that A=[0110] has no real eigenvalues.

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