Differential equation question.

Thank you.

Exercise 2. For the matrix 2 A = 4 2 -1 do the following: (a) Show that A = 2 is an eigenvalue, and use it to find an eigenvector v. (b) Show that, for your eigenvalue/eigenvector pair you found in part (a), the vector function x(t) = vest solves the linear, homogeneous constant coefficients 3 x 3 system of ODEs x' = Ax