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let-give-the-matrice-A-1-0-0-0-1-1-1-0-1-A-M-3-R-write-A-at-form-A-I-J-and-calcula




Question Number 28369 by abdo imad last updated on 24/Jan/18
let give the matrice   A =  (((1      0      0)),((0       1      1)) )                 [                                        (1        0      1  A ∈ M_3 (R)  write  A at form  A= I +J    and calculate  A^n .
$${let}\:{give}\:{the}\:{matrice}\:\:\:{A}\:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\right.\right. \\ $$$${A}\:\in\:{M}_{\mathrm{3}} \left({R}\right)\:\:{write}\:\:{A}\:{at}\:{form}\:\:{A}=\:{I}\:+{J}\:\:\:\:{and}\:{calculate} \\ $$$${A}^{{n}} . \\ $$

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