Question

x⃗ ′=[−2−1 1−4]x⃗ Find the most general real-valued solution to the linear system of differential equations

Answer 1

If you watched the video I linked you to earlier, this will be no problem for you.

Find the eigenvalues and hence eigenvectors. Therefore find the two linearly independent solutions of the ODE. Finally, write down an arbitrary linear combination of the two; that's the general answer.