The general solution of the linear system x = Ax is et/4 X(t) = | C1 et/3 C2 Determine the constant coefficient matrix A.
The general solution of the linear system x = Ax is et/4 X(t) = | C1 et/3 C2 Determine the constant coefficient matrix A.
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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![The general solution of the linear system \(\dot{\vec{x}} = A\vec{x}\) is
\[
\vec{x}(t) =
\begin{bmatrix}
e^{t/4} & 0 \\
0 & e^{t/3}
\end{bmatrix}
\begin{bmatrix}
c_1 \\
c_2
\end{bmatrix}.
\]
Determine the constant coefficient matrix \(A\).
\[
A =
\begin{bmatrix}
\boxed{\phantom{x}} & \boxed{\phantom{x}} \\
\boxed{\phantom{x}} & \boxed{\phantom{x}}
\end{bmatrix}
\]
[help (matrices)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31330aa5-a64b-4d2f-80e6-6ea74abb2a34%2F372df411-1e8d-4c78-99b7-a18f92996191%2Fkv3tqn4_processed.png&w=3840&q=75)
Transcribed Image Text:The general solution of the linear system \(\dot{\vec{x}} = A\vec{x}\) is
\[
\vec{x}(t) =
\begin{bmatrix}
e^{t/4} & 0 \\
0 & e^{t/3}
\end{bmatrix}
\begin{bmatrix}
c_1 \\
c_2
\end{bmatrix}.
\]
Determine the constant coefficient matrix \(A\).
\[
A =
\begin{bmatrix}
\boxed{\phantom{x}} & \boxed{\phantom{x}} \\
\boxed{\phantom{x}} & \boxed{\phantom{x}}
\end{bmatrix}
\]
[help (matrices)]
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