let-give-A-1-n-n-1-with-n-N-and-R-find-lim-n-A-n-

Tinku Tara June 4, 2023 Matrices and Determinants 0 Comments

Question Number 28678 by abdo imad last updated on 28/Jan/18

let give A= (((1 (α/n))),((−(α/n) 1)) ) with n ∈N^∗ and α∈R find lim_(n→+∞) A^n .

$${let}\:{give}\:{A}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\frac{\alpha}{{n}}}\\{−\frac{\alpha}{{n}}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${with}\:{n}\:\in{N}^{\ast} \:\:{and}\:\alpha\in{R}\:\:\:{find}\:\:{lim}_{{n}\rightarrow+\infty} {A}^{{n}} \:\:. \\ $$

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