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How can prove this

[tex]\exp(At)\exp(-At_0)=\exp(A(t-t_0))[/tex]?

using [tex]\displaystyle\sum_{i=0}^n{(1/k!)A^kt^k}[/tex]

and this properties

in t=0

[tex]

[\exp(At)]_{t} = I

[/tex]

[tex]exp(At)exp(-At)=I[/tex]

[tex]\frac{dexp(At)}{dt}=Aexp(At)=exp(At)A[/tex]

[tex]\exp(At)\exp(-At_0)=\exp(A(t-t_0))[/tex]?

using [tex]\displaystyle\sum_{i=0}^n{(1/k!)A^kt^k}[/tex]

and this properties

in t=0

[tex]

[\exp(At)]_{t} = I

[/tex]

[tex]exp(At)exp(-At)=I[/tex]

[tex]\frac{dexp(At)}{dt}=Aexp(At)=exp(At)A[/tex]

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