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Category: Matrices and Determinants

Soit-a-b-c-et-4-nombres-rationnels-telque-1-3-est-irrationnel-Demontrer-que-a-1-3-b-1-3-c-a-b-c-

Question Number 148446 by puissant last updated on 28/Jul/21 $$\mathrm{Soit}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{et}\:\alpha\:\mathrm{4}\:\mathrm{nombres}\:\mathrm{rationnels} \\ $$$$\mathrm{telque}\:\sqrt[{\mathrm{3}}]{\alpha}\:\mathrm{est}\:\mathrm{irrationnel}.. \\ $$$$\mathrm{Demontrer}\:\mathrm{que}\:: \\ $$$$\left(\mathrm{a}\sqrt[{\mathrm{3}}]{\alpha}+\mathrm{b}\sqrt[{\mathrm{3}}]{\alpha}=\mathrm{c}\right)\:\Rightarrow\:\left(\mathrm{a}=\mathrm{b}=\mathrm{c}\right).. \\ $$ Commented by Olaf_Thorendsen last updated on 28/Jul/21…

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Question Number 78670 by berket last updated on 19/Jan/20 $${let}\:{A}=\begin{bmatrix}{{a}\:\:{b}}\\{{c}\:\:{d}}\end{bmatrix}{use}\:{the}\:{augmented}\:{matrix}\left[{A}\:{I}\right]\:{and}\:{elementary}\:{row}\:{operation}\:{to}\:{show}\:{A}^{−\mathrm{1}} =\:\frac{\mathrm{1}}{{ad}\:{bc}}\begin{bmatrix}{{a}\:\:{b}}\\{{c}\:\:\:{d}}\end{bmatrix}{and}\:{show}\:{that}\:{det}\left({A}^{−\mathrm{1}} \right)=\frac{\mathrm{1}}{{det}\left({A}\right)} \\ $$$$ \\ $$ Commented by abdomathmax last updated on 20/Jan/20 $${Pc}\left({A}\right)={det}\left({A}−{xI}\right)\:=\begin{vmatrix}{{a}−{x}\:\:\:\:\:\:\:{b}}\\{{c}\:\:\:\:\:\:\:\:\:\:{d}−{x}}\end{vmatrix} \\…

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Question Number 346 by 123456 last updated on 25/Jan/15 $$\Gamma\left(\theta\right)=\begin{bmatrix}{\mathrm{cos}\:\theta}&{\mathrm{sin}\:\theta}\\{−\mathrm{sin}\:\theta}&{\mathrm{cos}\:\theta}\end{bmatrix} \\ $$$$\Lambda\left(\theta,{t}\right)=\begin{bmatrix}{\mathrm{cos}\:\theta}&{\mathrm{sinh}\:{t}\:\mathrm{sin}\:\theta}\\{\mathrm{sin}\:\theta}&{\mathrm{cosh}\:{t}\:\mathrm{cos}\:\theta}\end{bmatrix} \\ $$$$\zeta\left(\theta,{t}\right)=\Gamma\left(\theta\right)×\Lambda\left(\theta,{t}\right)+\Lambda\left(\theta,{t}\right)×\Gamma\left(\theta\right) \\ $$$$\zeta\left(\theta,\mathrm{0}\right)=? \\ $$$$\mathrm{det}\:\zeta\left(\theta,\mathrm{0}\right)=? \\ $$ Answered by prakash jain last…