I'm trying to figure out if I am doing this correctly.
Given the matrix A:
write down e^(tA) and calculate e^(tA)X, X = (1,1)
So far what I did was, I found the eigenvalues (1.5 repeated) and the eigenvectors ( [-1 1], [1 1]). (The eigenvectors are transposed)
Then I set e^(tA) = T^(-1)AT, where T = [eigenvector1, eigenvector 2]
Which leads to e^(tA):
I Feel that I do not have the correct equation for e^(tA), can anyone help me?