Category: Matrices and Determinants

Question Number 202371 by mnjuly1970 last updated on 25/Dec/23 $$$$$$IfA\in M_{2\times 2},det\left(A\right)\ne 0$$$$,A^3=A^2+A\Rightarrow Findthe$$$$valuesofdet(2A-I)$$$$$$ Answered by…

Question Number 199164 by mnjuly1970 last updated on 28/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 199001 by mnjuly1970 last updated on 26/Oct/23 $$$$$$\mathrm{I}f,\mathrm{A}\in {\mathrm{M}}_{n\times n},{\mathrm{A}}^2=\mathrm{A},1\ne k\in \mathbb{R}.$$$$\mathrm{F}ind{(\mathrm{I}-k\mathrm{A})}^{-1}=?$$ Answered by MM42 last updated on…

Question Number 198156 by Erico last updated on 12/Oct/23 $$\mathrm{Prove}\mathrm{that}$$$$\frac{2\mathrm{t}-1}{\mathrm{lnt}-\ln (1-\mathrm{t})}={\underset{0}{\int }}^1{\mathrm{t}}^{\mathrm{x}}{(1-\mathrm{t})}^{1-\mathrm{x}}\mathrm{dx}$$$$\mathrm{and}{\underset{0}{\int }}^1\frac{2\mathrm{t}-1}{\mathrm{lnt}-\ln (1-\mathrm{t})}\mathrm{dt}=\frac{\pi }{2}{\underset{0}{\int }}^1\frac{\mathrm{x}(1-\mathrm{x})}{\sin \left(\pi \mathrm{x}\right)}\mathrm{dx}$$ Answered…

Question Number 195185 by Erico last updated on 26/Jul/23 $$1/\mathrm{Montrer}\mathrm{que}{\underset{0}{\int }}^{+\mathrm{\infty }}\frac{{(1-x^2)}^{2p-1}}{1-x^{4p}}dx=\left(\frac{2^{2p-3}}{p}\right)\pi [1+2\underset{k=1}{\sum ^{p-1}}{cos}^{2p-1}\left(\frac{k\pi }{2p}\right)]$$$$\mathrm{2}/\:\:\:\:\mathrm{En}\:\mathrm{d}\acute {\mathrm{e}duire}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}{p}−\mathrm{1}}…