Suppose A=PDP−1A = PDP^{-1}A=PDP−1 where D=diag(2,−1,4)D = \text{diag}(2, -1, 4)D=diag(2,−1,4). What is the matrix exponential eAe^AeA?
PeDP−1P e^D P^{-1}PeDP−1 where eD=diag(e2,e−1,e4)e^D = \text{diag}(e^2, e^{-1}, e^4)eD=diag(e2,e−1,e4)
etr(A)Ie^{\text{tr}(A)} Ietr(A)I
P[e2000e−1000e4]P−1P \begin{bmatrix} e^2 & 0 & 0 \\ 0 & e^{-1} & 0 \\ 0 & 0 & e^4 \end{bmatrix} P^{-1}Pe2000e−1000e4P−1
Both (a) and (c)