Computing matrix exponential e^Jt for Jordan form with repeated eigenvalue

[panoskarti]

ok this is my problem...
i have diagonalized the A matrix with the equation P^-1*A*P
and the result is J=[-1 0 0;0 2 1; 0 0 2]. in order to find the e^Jt do i need to do the following? =>


[-e^t t*e^t 1/2*t^2 *e^t

0 2*e^t t*e^t

0 0 2*e^t]


I am not sure about the 2 and 3 elements in the first row of the matrix since i have zeros at the J matrix but a mathematics book confused me..

Thanks in advance..

 

[panoskarti]

i did a mistake this is the matrix..

[e^-t t*e^t 1/2*t^2 *e^t

0 e^2t t*e^t

0 0 e^2t ]