Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1 2 9. A fundamental set of solutions of x': -3 -1 3 x is: 3 2 -2

1 2 9. A fundamental set of solutions of x': -3 -1 3 x is: 3 2 -2

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
See similar textbooks
icon
Related questions
Question
100%
**9. A fundamental set of solutions of \(\mathbf{x}' = \begin{pmatrix} 1 & 2 & 0 \\ -3 & -1 & 3 \\ 3 & 2 & -2 \end{pmatrix} \mathbf{x}\) is:** \( \text{(a)} \quad \mathbf{x}_1 = e^{-2t} \begin{pmatrix} 2 \\ -3 \\ 3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \) \( \text{(b)} \quad \mathbf{x}_1 = e^{2t} \begin{pmatrix} 2 \\ -3 \\ 3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix} \) \( \text{(c)} \quad \mathbf{x}_1 = e^{2t} \begin{pmatrix} 2 \\ 3 \\ -3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} -1 \\ -1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix} \) \( \text{(d)} \quad \mathbf{x}_1 = e^{-2t} \begin{pmatrix} -2 \\ 3 \\ -3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} 1 \\ 1 \\ -1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \) \( \text{(e)} \quad \text{None of the
Transcribed Image Text:**9. A fundamental set of solutions of \(\mathbf{x}' = \begin{pmatrix} 1 & 2 & 0 \\ -3 & -1 & 3 \\ 3 & 2 & -2 \end{pmatrix} \mathbf{x}\) is:** \( \text{(a)} \quad \mathbf{x}_1 = e^{-2t} \begin{pmatrix} 2 \\ -3 \\ 3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \) \( \text{(b)} \quad \mathbf{x}_1 = e^{2t} \begin{pmatrix} 2 \\ -3 \\ 3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix} \) \( \text{(c)} \quad \mathbf{x}_1 = e^{2t} \begin{pmatrix} 2 \\ 3 \\ -3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} -1 \\ -1 \\ 1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix} \) \( \text{(d)} \quad \mathbf{x}_1 = e^{-2t} \begin{pmatrix} -2 \\ 3 \\ -3 \end{pmatrix}, \quad \mathbf{x}_2 = e^{-t} \begin{pmatrix} 1 \\ 1 \\ -1 \end{pmatrix}, \quad \mathbf{x}_3 = e^{t} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \) \( \text{(e)} \quad \text{None of the
Expert Solution
steps

Step by step

Solved in 8 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS