For a discrete dynamic system in R
4
. a) [2pt] Find V and D so that T=VDV
∧
(−1). Hint: use a built-in Matlab function to do this in one step. Answer the following questions by working with V and D rather than T directly (though you can double-check your answer with T). b) [3pt] Find a stationary x for T, that is an x so that Tx=x, and explain how you found it. Note: don't work with T directly, work with V and D. c) [3pt] Find an x so that a
n
=T
n
x diverges, that is, becomes arbitrarily large, as n goes to infinity. Explain how you found it. Note: don't work with T directly, work with V and D. d) [3pt] Find an x so that a
n
=T
n
x decays, that is becomes arbitrarily close to 0 , as n goes to infinity. Explain how you found it. Note: don't work with T directly, work with V and D. e) [4pt] Consider the vector u=[1.56558010815612;8.34207951426251;−9.44911182523058;−1.43127456785804