Let $ A = \begin{pmatrix} 1 & 2 \\ 0 & -1 \end{pmatrix} $ whose eigenvalues and eigenvectors are $ r_1 = 1, \, \mathbf{u}_1 = \begin{pmatrix} 1 \\ 0 \end{pmatrix} $ and $ r_2 = -1, \, \mathbf{u}_2 = \begin{pmatrix} 1 \\ -1 \end{pmatrix} $.Find $ e^{At} = \begin{pmatrix} a(t) & b(t) \\ c(t) & d(t) \end{pmatrix} $.- **a(t)**: [Choose]- **b(t)**: [Choose]- **c(t)**: [Choose]- **d(t)**: [Choose]

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Answered: 2 whose eigenvalues and eigenvectors…

2 whose eigenvalues and eigenvectors are ri = 1, ui and r2 = -1, u2 Let A = ´a(t) b(t) ( dt). Find eAt a(t) ( Choose ) b(t) (Choose ] c(t) [ Choose ) d(t) ( Choose ) > > >

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 $ A = \begin{pmatrix} 1 & 2 \\ 0 & -1 \end{pmatrix} $ whose eigenvalues and eigenvectors are $ r_1 = 1, \, \mathbf{u}_1 = \begin{pmatrix} 1 \\ 0 \end{pmatrix} $ and $ r_2 = -1, \, \mathbf{u}_2 = \begin{pmatrix} 1 \\ -1 \end{pmatrix} $.

Find $ e^{At} = \begin{pmatrix} a(t) & b(t) \\ c(t) & d(t) \end{pmatrix} $.

- **a(t)**: [Choose]
- **b(t)**: [Choose]
- **c(t)**: [Choose]
- **d(t)**: [Choose]

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