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

Tinku Tara June 4, 2023 Algebra 0 Comments

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

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) .

$${let}\:\:{A}\:=\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:\:{P}\:{inversible}\:{and}\:{D}\:{diagoanal}\:{in}\:{ordre}\:{to}\:{have} \\ $$$${A}\:={PDP}^{−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{with}\:{n}\:{integr}\:{nstural} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{e}^{{t}\:{A}} \:\:\:{with}\:{t}\:\in\:{R}\:\: \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{e}^{−{A}} \:\:. \\ $$

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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

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