Question Number 37230 by abdo.msup.com last updated on 11/Jun/18
$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}}\end{pmatrix} \\ $$$${calculate}\:\:{A}^{{n}} \: \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:\:,\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\:{e}^{{iA}} ,\:{e}^{−{iA}} \:\:\:{and}\:{e}^{{iA}} \:+{e}^{−{iA}} \:\:. \\ $$