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}0 & (t+8) e^{-3 t} \ e^{-3 t} & e^{-3 t}\end{array}\right) $
B) $ \Psi(t)=\left(\begin{array}{ll}e^{3 t} & 8(t+8) e^{3 t} \ 0 & e^{3 t}\end{array}\right) $
C) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t}(t+8) e^{-3 t} \ 0 & e^{-3 t}\end{array}\right) $
D) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t} & e^{-3 t} \ 0 & (t+8) e^{-3 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}0 & (t+8) e^{-3 t} \ e^{-3 t} & e^{-3 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}e^{3 t} & 8(t+8) e^{3 t} \ 0 & e^{3 t}\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t}(t+8) e^{-3 t} \ 0 & e^{-3 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t} & e^{-3 t} \ 0 & (t+8) e^{-3 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}0 & (t+8) e^{-3 t} \ e^{-3 t} & e^{-3 t}\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}e^{3 t} & 8(t+8) e^{3 t} \ 0 & e^{3 t}\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t}(t+8) e^{-3 t} \ 0 & e^{-3 t}\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{ll}e^{-3 t} & e^{-3 t} \ 0 & (t+8) e^{-3 t}\end{array}\right) $

Consider the First-Order Homogeneous System of Linear Differential Equations ψ(t)=(0(t+8)e−3te−3te−3t) \psi(t)=\left(\begin{array}{ll}0 & (t+8) e^{-3 t} \\ e^{-3 t} & e^{-3 t}\end{array}\right) ψ(t)=(0e−3t​(t+8)e−3te−3t​)

Consider the First-Order Homogeneous System of Linear Differential Equations
$\psi(t)=\left(\begin{array}{ll}0 & (t+8) e^{-3 t} \\ e^{-3 t} & e^{-3 t}\end{array}\right)$