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}-\sin (3 t) & \cos (3 t) \ \cos (3 t) & -\sin (3 t)\end{array}\right) $
B) $ \Psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ -\cos (3 t) & \sin (3 t)\end{array}\right) $
C) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & \cos (3 t) \ \cos (3 t) & \sin (3 t)\end{array}\right) $
D) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ \cos (3 t) & \sin (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}-\sin (3 t) & \cos (3 t) \ \cos (3 t) & -\sin (3 t)\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ -\cos (3 t) & \sin (3 t)\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & \cos (3 t) \ \cos (3 t) & \sin (3 t)\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ \cos (3 t) & \sin (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}-\sin (3 t) & \cos (3 t) \ \cos (3 t) & -\sin (3 t)\end{array}\right) $ 
B) $ \Psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ -\cos (3 t) & \sin (3 t)\end{array}\right) $ 
C) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & \cos (3 t) \ \cos (3 t) & \sin (3 t)\end{array}\right) $ 
D) $ \psi(t)=\left(\begin{array}{ll}\sin (3 t) & -\cos (3 t) \ \cos (3 t) & \sin (3 t)\end{array}\right] $

Consider the First-Order Homogeneous System of Linear Differential Equations ψ(t)=(−sin⁡(3t)cos⁡(3t)cos⁡(3t)−sin⁡(3t)) \psi(t)=\left(\begin{array}{ll}-\sin (3 t) & \cos (3 t) \\ \cos (3 t) & -\sin (3 t)\end{array}\right) ψ(t)=(−sin(3t)cos(3t)​cos(3t)−sin(3t)​)

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