Consider the first-order nonhomogeneous system of linear differential equations

Where the components of g(t) are continuous functions.
Which of these is the fundamental matrix (t) for this system?
A) $ \psi(t)=\left(\begin{array}{l}e^{3 t}-3 e^{-1 t} \ e^{3 t} 1 e^{-1 t}\end{array}\right) $
B) $ \Psi(t)=\left(\begin{array}{l}e^{3 t} 3 e^{-1 t} \ e^{3 t}-1 e^{-1 t}\end{array}\right) $
C) $ \psi(t)=\left(\begin{array}{ll}-e^{3 t} & -1 e^{-1 t} \ e^{3 t} & 3 e^{-1 t}\end{array}\right) $
D) $ \psi(t)=\left(\begin{array}{l}e^{-3 t} 3 e^{-1 t} \ e^{-3 t}-1 e^{-1 t}\end{array}\right) $

Question

Consider the first-order nonhomogeneous system of linear differential equations

Where the components of g(t) are continuous functions.
Which of these is the fundamental matrix  (t) for this system?
A) $ \psi(t)=\left(\begin{array}{l}e^{3 t}-3 e^{-1 t} \ e^{3 t} 1 e^{-1 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{l}e^{3 t} 3 e^{-1 t} \ e^{3 t}-1 e^{-1 t}\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}-e^{3 t} & -1 e^{-1 t} \ e^{3 t} & 3 e^{-1 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{l}e^{-3 t} 3 e^{-1 t} \ e^{-3 t}-1 e^{-1 t}\end{array}\right) $

Quizplus · Accepted Answer

The Answer of Consider the first-order nonhomogeneous system of linear differential equations

Where the components of g(t) are continuous functions.
Which of these is the fundamental matrix  (t) for this system?
A) $ \psi(t)=\left(\begin{array}{l}e^{3 t}-3 e^{-1 t} \ e^{3 t} 1 e^{-1 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{l}e^{3 t} 3 e^{-1 t} \ e^{3 t}-1 e^{-1 t}\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}-e^{3 t} & -1 e^{-1 t} \ e^{3 t} & 3 e^{-1 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{l}e^{-3 t} 3 e^{-1 t} \ e^{-3 t}-1 e^{-1 t}\end{array}\right) $

Consider the First-Order Nonhomogeneous System of Linear Differential Equations ψ(t)=(e3t−3e−1te3t1e−1t) \psi(t)=\left(\begin{array}{l}e^{3 t}-3 e^{-1 t} \\ e^{3 t} 1 e^{-1 t}\end{array}\right) ψ(t)=(e3t−3e−1te3t1e−1t​)

Consider the First-Order Nonhomogeneous System of Linear Differential Equations
$\psi(t)=\left(\begin{array}{l}e^{3 t}-3 e^{-1 t} \\ e^{3 t} 1 e^{-1 t}\end{array}\right)$