Hello everyone! I have just started to learn eigenvalues/vectors for solving systems in my Diff Eq class. I am really stumped on how you go from getting the values and vectors to solving an IVP. This is one of my HW questions. Could anyone help me out with going from the eigenvalues/vectors to the solution? For this case i get lambda1=0, lambda2 = 8. The vectors get kinda weird. Thanks in advance!

I cant get the LaTeX to work... the system is dx/dt = system [upper right = 8 upper left = 0 lower right = 8 lower left = 0] * x. Sorry for the confusing format