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Question Number 113549 by mathmax by abdo last updated on 13/Sep/20
let A  = (((1        −(1/n))),(((1/n)     1)) )  1) calculate A^2   2) calculate  A^m      (m  integr natural)  3) coclude A^n    and lim_(n→+∞)  A^n   4) calculate e^A  and e^(−A)
$$\mathrm{let}\:\mathrm{A}\:\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\frac{\mathrm{1}}{\mathrm{n}}}\\{\frac{\mathrm{1}}{\mathrm{n}}\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\:\mathrm{A}^{\mathrm{m}} \:\:\:\:\:\left(\mathrm{m}\:\:\mathrm{integr}\:\mathrm{natural}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{coclude}\:\mathrm{A}^{\mathrm{n}} \:\:\:\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \\ $$

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