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Category: Relation and Functions

let-A-1-2-1-1-1-calculste-A-n-2-determine-e-A-and-e-2A-3-find-cos-A-and-sinA-is-cos-2-A-sin-2-A-I-4-determine-sh-A-and-ch-A-is-ch-2-A-sh-2-A-I-

Question Number 91268 by mathmax by abdo last updated on 29/Apr/20 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\:{e}^{{A}} \:\:{and}\:{e}^{−\mathrm{2}{A}} \\ $$$$\left.\mathrm{3}\right){find}\:{cos}\left({A}\right){and}\:{sinA}\:\:\:{is}\:{cos}^{\mathrm{2}} {A}\:+{sin}^{\mathrm{2}} {A}\:={I}? \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{sh}\left({A}\right)\:{and}\:{ch}\left({A}\right)\:\:{is}\:{ch}^{\mathrm{2}} {A}−{sh}^{\mathrm{2}} {A}\:={I}\:\:?…