Consider the first-order homogeneous system of linear differential equations

Which of these is the fundamental matrix ?(t) for this system?
A) $ \psi(t)=\left(\begin{array}{ll}e^{4 t}-4 e^{-5 t} \ e^{4 t} 5 e^{-5 t}\end{array}\right) $
B) $ \Psi(t)=\left(\begin{array}{ll}-e^{4 t} & -5 e^{-5 t} \ e^{4 t} & 4 e^{-5 t}\end{array}\right) $
C) $ \Psi(t)=\left(\begin{array}{l}e^{4 t} 4 e^{-5 t} \ e^{4 t}-5 e^{-5 t}\end{array}\right) $
D) $ \psi(t)=\left(\begin{array}{l}e^{-4 t} 4 e^{-5 t} \ e^{-4 t}-5 e^{-5 t}\end{array}\right) $

Question

Consider the first-order homogeneous system of linear differential equations
 
Which of these is the fundamental matrix ?(t) for this system?
A) $ \psi(t)=\left(\begin{array}{ll}e^{4 t}-4 e^{-5 t} \ e^{4 t} 5 e^{-5 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}-e^{4 t} & -5 e^{-5 t} \ e^{4 t} & 4 e^{-5 t}\end{array}\right) $ 
C) $ \Psi(t)=\left(\begin{array}{l}e^{4 t} 4 e^{-5 t} \ e^{4 t}-5 e^{-5 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{l}e^{-4 t} 4 e^{-5 t} \ e^{-4 t}-5 e^{-5 t}\end{array}\right) $

Quizplus · Accepted Answer

The Answer of Consider the first-order homogeneous system of linear differential equations
 
Which of these is the fundamental matrix ?(t) for this system?
A) $ \psi(t)=\left(\begin{array}{ll}e^{4 t}-4 e^{-5 t} \ e^{4 t} 5 e^{-5 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}-e^{4 t} & -5 e^{-5 t} \ e^{4 t} & 4 e^{-5 t}\end{array}\right) $ 
C) $ \Psi(t)=\left(\begin{array}{l}e^{4 t} 4 e^{-5 t} \ e^{4 t}-5 e^{-5 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{l}e^{-4 t} 4 e^{-5 t} \ e^{-4 t}-5 e^{-5 t}\end{array}\right) $

Consider the First-Order Homogeneous System of Linear Differential Equations ψ(t)=(e4t−4e−5te4t5e−5t) \psi(t)=\left(\begin{array}{ll}e^{4 t}-4 e^{-5 t} \\ e^{4 t} 5 e^{-5 t}\end{array}\right) ψ(t)=(e4t−4e−5te4t5e−5t​)

Consider the First-Order Homogeneous System of Linear Differential Equations
$\psi(t)=\left(\begin{array}{ll}e^{4 t}-4 e^{-5 t} \\ e^{4 t} 5 e^{-5 t}\end{array}\right)$