Consider the First-Order Homogeneous System of Linear Differential Equations
$\alpha$

Multiple Choice

Consider the first-order homogeneous system of linear differential equations

Which of these statements is true?

A) For any real number $\alpha$ , the eigenvalues for this system are real numbers.
B) For -8 < $\alpha$ < 0, the trajectories spiral towards the origin as t $\rightarrow$$\infty$ .
C) For $\alpha$ < -8, the trajectories spiral away from the origin as t $\rightarrow$$\infty$ .
D) For $\alpha$ = 8, the eigenvalues are purely imaginary and the trajectories are concentric circles centered at the origin.