Calculating exp(At): Reverse Laplace Transform vs. Matrix Series Method

[erezb84]

Homework Statement

I have the following matrix:
A=[0 -1; 0 -1]

and i need to calculate: exp(At) in several ways, 2 of them are using the reverse Laplace transform and using: I + Ʃ(A^kt^k)/k!

i have tried to start the series but i am getting an expression that i can't say which series it is,
and when i try with Laplace i get the one of the matrix expressions is a step function..

i will apreaciate the help...

thanks!

 

[RoshanBBQ]

What are you getting for
$$(sI-A)^{-1}$$

 

[erezb84]

this is what i get. but i can't find the reverse transform...

 

[RoshanBBQ]

this is what i get. but i can't find the reverse transform...

You are dividing by the wrong thing. Divide by
$$s(s+1)$$
instead of
$$s(s+1)-1$$

 

[erezb84]

but
$$s(s+1)-1$$
is the deteminante..
in oreder to reverse 2*2 matrix i do this:
[a b ; c d]^-1 = [d -b; -c a] * 1/det
no?

 

[RoshanBBQ]

but
$$s(s+1)-1$$
is the deteminante..
In oreder to reverse 2*2 matrix i do this:
[a b ; c d]^-1 = [d -b; -c a] * 1/det
no?

1*0 = 0

 

[erezb84]

daaaam! right, thanks!