How do I solve for exp(A*t) using a fundamental matrix?

I am trying to compute e^tA using a fundamental matrix. I am not sure if this is the correct path so far, I am getting very large numbers for all of my vectors. Assuming those are the constants I know need to find the inverse of psi(0) to multiply it to the psi(t) matrix. Please help! Here is my code so far:

syms t;
A=[1 1 1;2 1 -1;-8 -5 -3]
Eig=eig(A)
eig1=Eig(1,:)
eig2=Eig(2,:)
eig3=Eig(3,:)
[V,D]=eig(A)
V1=V(:,1)
V2=V(:,2)
V3=V(:,3)
x1=exp(eig1*t)*V1
x2=exp(eig2*t)*V2
x3=exp(eig3*t)*V3
psi(t)=[x1 x2 x3]

Answer 1

[Star Strider]

If I understand correctly what you want to do, use the expm (link) function.