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) calculate e^(−A) .


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

$l e t A = (\begin{matrix} 2 1 \\ - 1 1 \end{matrix})$ $1) d e t e r m i n e P i n v e r s i b l e a n d D d i a g o a n a l i n o r d r e t o h a v e$ $A = {P D P}^{- 1}$ $1) c a l c u l a t e A^{n} w i t h n i n t e g r n s t u r a l$ $2) c a l c u l a t e e^{t A} w i t h t \in R$ $3) c a l c u l a t e e^{- A} .$
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