Let *₁(t) = Show that r₁(t) is a solution to the 9 P-4 2e³t+4e-t 3e³t+10e 100-1], #₂(t) = -4e³t+2e- -6e³t + 5e¯ system P by evaluating derivatives and the matrix product = x' 9 *{(t) = [1/5 = 1(t) Enter your answers in terms of the variable t. [ AH Show that 2 (t) is a solution to the system' help (formulas) help (matrices) Pa by evaluating derivatives and the matrix product 9 2 {(t) = [153 = √²2(1)
Let *₁(t) = Show that r₁(t) is a solution to the 9 P-4 2e³t+4e-t 3e³t+10e 100-1], #₂(t) = -4e³t+2e- -6e³t + 5e¯ system P by evaluating derivatives and the matrix product = x' 9 *{(t) = [1/5 = 1(t) Enter your answers in terms of the variable t. [ AH Show that 2 (t) is a solution to the system' help (formulas) help (matrices) Pa by evaluating derivatives and the matrix product 9 2 {(t) = [153 = √²2(1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
9. Ordinary
![Let
\[ P = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix}, \]
\[ \vec{x}_1(t) = \begin{bmatrix} 2e^{3t} + 4e^{-t} \\ 3e^{3t} + 10e^{-t} \end{bmatrix}, \quad \vec{x}_2(t) = \begin{bmatrix} -4e^{3t} + 2e^{-t} \\ -6e^{3t} + 5e^{-t} \end{bmatrix}. \]
Show that \( \vec{x}_1(t) \) is a solution to the system \( \vec{x}' = P\vec{x} \) by evaluating derivatives and the matrix product
\[ \vec{x}_1'(t) = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix} \vec{x}_1(t) \]
Enter your answers in terms of the variable \( t \).
\[ \begin{bmatrix} \quad \end{bmatrix} = \begin{bmatrix} \quad \end{bmatrix} \]
\[ \text{help (formulas)} \quad \text{help (matrices)} \]
Show that \( \vec{x}_2(t) \) is a solution to the system \( \vec{x}' = P\vec{x} \) by evaluating derivatives and the matrix product
\[ \vec{x}_2'(t) = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix} \vec{x}_2(t) \]
Enter your answers in terms of the variable \( t \).
\[ \begin{bmatrix} \quad \end{bmatrix} = \begin{bmatrix} \quad \end{bmatrix} \]
\[ \text{help (formulas)} \quad \text{help (matrices)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F8414eaef-900e-41c3-9f61-daddc66cae2f%2Fn6yeti_processed.png&w=3840&q=75)
Transcribed Image Text:Let
\[ P = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix}, \]
\[ \vec{x}_1(t) = \begin{bmatrix} 2e^{3t} + 4e^{-t} \\ 3e^{3t} + 10e^{-t} \end{bmatrix}, \quad \vec{x}_2(t) = \begin{bmatrix} -4e^{3t} + 2e^{-t} \\ -6e^{3t} + 5e^{-t} \end{bmatrix}. \]
Show that \( \vec{x}_1(t) \) is a solution to the system \( \vec{x}' = P\vec{x} \) by evaluating derivatives and the matrix product
\[ \vec{x}_1'(t) = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix} \vec{x}_1(t) \]
Enter your answers in terms of the variable \( t \).
\[ \begin{bmatrix} \quad \end{bmatrix} = \begin{bmatrix} \quad \end{bmatrix} \]
\[ \text{help (formulas)} \quad \text{help (matrices)} \]
Show that \( \vec{x}_2(t) \) is a solution to the system \( \vec{x}' = P\vec{x} \) by evaluating derivatives and the matrix product
\[ \vec{x}_2'(t) = \begin{bmatrix} 9 & -4 \\ 15 & -7 \end{bmatrix} \vec{x}_2(t) \]
Enter your answers in terms of the variable \( t \).
\[ \begin{bmatrix} \quad \end{bmatrix} = \begin{bmatrix} \quad \end{bmatrix} \]
\[ \text{help (formulas)} \quad \text{help (matrices)} \]
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