let-A-2-1-1-1-1-determine-P-inversible-and-D-diagoanal-in-ordre-to-have-A-PDP-1-1-calculate-A-n-with-n-integr-nstural-2-calculate-e-t-A-with-t-R-3

Question Number 53775 by maxmathsup by imad last updated on 25/Jan/19

l e t A = (\begin{matrix} 2 1 \\ - 1 1 \end{matrix})

1) d e t e r m i n e P i n v e r s i b l e a n d D d i a g o a n a l i n o r d r e t o h a v e

A = {P D P}^{- 1}

1) c a l c u l a t e A^{n} w i t h n i n t e g r n s t u r a l

2) c a l c u l a t e e^{t A} w i t h t \in R

3) c a l c u l a t e e^{- A} .