Steps from state space to transfer function

[Std]

Homework Statement

What is the diffetence between steps of solving the question
x'= [matrix values]x +[vector values]u
and solving the question
x(k)=[matrix values]x(k-1) + [vector values]u

Relevant Equations

Transfer function= c*[SI-A]^-1*B

I mean the first question has derivative form and the second is linear form so what the difference here in steps of converting both to transfer function... please need some ellaboration to make sure i am solving correctly or not... is it correct to apply the same rule on both:
Transfer function= c*[SI-A]^-1*B
And when do we need to use laplace ?

 

[DaveE]

Laplace transforms are used (mostly) for continuous time systems.
Have you studied z-transforms yet?

 

[Std]

Thx for the reply... actually i am studying it from online resources and what i found for both cases are

So i cannot tell the difference between steps of both linear and continous... they seem similar to me... and no laplace is used in those steps and that is what is confusing me ... so is there laplace in any step that i missed here? Thanks again 4 ur help

 

[Std]

For example do these two questions have same steps of getting their transfer functions

I mean what i did for both is getting
Transfer fun= C*[SI-A]-1*B
Am i correct?