Question Number 30783 by math1967 last updated on 25/Feb/18 $${Prove}\:{that}\begin{vmatrix}{\mathrm{3}}&{{a}+{b}+{c}}&{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }\\{{a}+{b}+{c}}&{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }&{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }\\{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }&{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }&{{a}^{\mathrm{4}}…
Question Number 161429 by greg_ed last updated on 17/Dec/21 $$\mathrm{help}\:\mathrm{me}\:! \\ $$$$\begin{cases}{{x}+\mathrm{3}{y}+{z}=\mathrm{2}}\\{−\mathrm{3}{x}+\mathrm{4}{y}+\mathrm{2}{z}=\mathrm{3}}\\{−\mathrm{2}{x}+\mathrm{7}{y}+\mathrm{3}{z}=\mathrm{5}}\end{cases} \\ $$$$\boldsymbol{\mathrm{G}}\mathrm{auss}\:\mathrm{Method}… \\ $$ Commented by 1549442205PVT last updated on 18/Dec/21 $${the}\:{given}\:{system}\:{of}\:{equations}\:{is}\:{not} \\…
Question Number 30191 by abdo imad last updated on 17/Feb/18 $${let}\:{give}\:\:{A}\:=\:\begin{pmatrix}{\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\right) \\ $$$${calculate}\:{A}^{{n}} \:\:{and}\:\:{e}^{−{A}} \:\:. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 95260 by i jagooll last updated on 24/May/20 $$\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}+\mathrm{2y}−\mathrm{1}=\mathrm{0}\:\mathrm{transformed} \\ $$$$\mathrm{by}\:\mathrm{matrix}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{a}}\\{\mathrm{b}\:\:\:\mathrm{2}}\end{pmatrix}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{2x}+\mathrm{8y}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}×\mathrm{b}×\mathrm{c}\: \\ $$ Commented by mr W last updated…
Question Number 29032 by abdo imad last updated on 03/Feb/18 $$ \\ $$$${let}\:{give}\:{A}\:=\:\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}^{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{tA}} \:\:. \\ $$ Terms of Service…
Question Number 29029 by abdo imad last updated on 03/Feb/18 $${let}\:{give}\:{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{4}\:\:\:\:\:\:\:−\mathrm{3}}\end{pmatrix}\:\:{calculate}\:{A}^{{n}} \:{and}\:{e}^{{A}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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).\:\:\:\:\:…