Question Number 28678 by abdo imad last updated on 28/Jan/18 $${let}\:{give}\:{A}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\frac{\alpha}{{n}}}\\{−\frac{\alpha}{{n}}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${with}\:{n}\:\in{N}^{\ast} \:\:{and}\:\alpha\in{R}\:\:\:{find}\:\:{lim}_{{n}\rightarrow+\infty} {A}^{{n}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28261 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:{the}\:{matrice} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\mathrm{0}\:\:\:\:\:\:\:{cos}\theta\:\:\:\:\:\:{cos}\left(\mathrm{2}\theta\right)\right) \\ $$$${A}=\:\:\:\left(\:{cos}\theta\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:{cos}\left(\mathrm{2}\theta\right)\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left(\:{cos}\left(\theta\right)\:{cos}\left(\mathrm{2}\theta\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\right)\right. \\ $$$${and}\:{D}_{\theta} \:\:={det}\:{A}\:\:{solve}\:{inside}\:{R}\:\:{D}_{\theta} =\mathrm{0} \\ $$$$\:\:\:\: \\ $$$$\:…
Question Number 28259 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:\:\:\:{A}=\:\:\:\left(\:\:{cos}\theta\:\:\:\:\:\:\:−{sin}\theta\:\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:{sin}\theta\:\:\:\:\:\:\:\:\:{cos}\theta\:\:\:\:\right) \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:^{{t}} {A}.\:{A}\:\:.{prove}\:{that}\:{A}\:{is}\:{inversible}\:{and}\:{find} \\ $$$${A}^{−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:\:{A}^{{n}} \:\:\:{for}\:{n}\in\:{N} \\ $$$$\left.\mathrm{3}\right)\:{developp}\:\left({A}\:+{A}^{−\mathrm{1}} \right)^{{n}} \:\:{then}\:{prove}\:{that}…
Question Number 28260 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:\:\:\:\left(\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:−\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{A}=\:\:\:\:\:\left(\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:−\mathrm{1}\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\right) \\ $$$${and}\:{the}\:{matrices}\:\:{I}=\:\:\left(\:\:\mathrm{1}\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{0}\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{0}\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\:\right) \\ $$$${and}\:\:{J}=\:\:\:\left(\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:−\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{1}\right).\:\:\:\:\:…
Question Number 28257 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:\:−\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{A}\:\:\:\:\:=\:\:\:\:\:\:\left(\:\:−\mathrm{1}\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\right)\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:−\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\right)\: \\ $$$${find}\:{a}\:{diagoal}\:{matrice}\:{D}\:{and}\:{a}\:{inversible}\:{matrice}\:{P}\:\:{wich} \\ $$$${verify}\:{A}\:\:=\:{P}.{D}.{P}^{−\mathrm{1}} \:\:\:{and}\:\:{calculate}\:{A}^{{n}} . \\ $$…
Question Number 28258 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:{A}\:\:=\:\left(\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\mathrm{2}\:\:\:\:−\mathrm{1}\right) \\ $$$$\:\:{find}\:\:{e}^{{A}\:} \:\:\:\:{and}\:\:\:{e}^{−{tA}} .\:\: \\ $$ Commented by abdo imad last updated…
Question Number 28256 by abdo imad last updated on 22/Jan/18 $$\left.{let}\:{give}\:\:\:{A}=\:\:_{\:\:\:\:\left(\right.} \:−\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}\:\:\:\:\mathrm{1}\right)\:\:\:\:\:\:\:{find}\:\:{A}^{{n}} \:\:{for}\:{n}\:{integr}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:−\mathrm{1}\right) \\ $$$$\:\:\:\: \\ $$ Terms of Service Privacy…
Question Number 28255 by abdo imad last updated on 22/Jan/18 $${let}\:{give}\:{p}=\left(_{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:−\mathrm{2}} ^{\mathrm{1}\:\:\:\:\:\:\:\:\:\:−\mathrm{1}} \:\:\right)\:\:{and}\:\:{D}=\:\:\left(_{\mathrm{3}\:\:\:\:\:\:\:\:\:\:−\mathrm{6}} ^{\mathrm{2}\:\:\:\:\:\:\:\:−\mathrm{2}} \:\right)\:{calculate} \\ $$$${A}=\:{p}.{D}.{p}^{−\mathrm{1}} \:. \\ $$ Terms of Service Privacy Policy…
Question Number 159222 by physicstutes last updated on 14/Nov/21 $$\mathrm{find}\:\mathrm{an}\:\mathrm{explicit}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{4}}{\mathrm{5}},\:\frac{\mathrm{8}}{\mathrm{9}},\:\frac{\mathrm{16}}{\mathrm{17}},\:\frac{\mathrm{32}}{\mathrm{33}},\:… \\ $$ Commented by MJS_new last updated on 14/Nov/21 $${a}_{{n}} =\mathrm{1}−\frac{\mathrm{12}}{{n}^{\mathrm{4}}…
Question Number 93493 by i jagooll last updated on 13/May/20 Commented by i jagooll last updated on 13/May/20 $$\mathrm{it}\:\mathrm{is}\:\mathrm{my}\:\mathrm{method}\:\mathrm{sir}\:\mathrm{Rio}\: \\ $$ Commented by i jagooll…