Category: Matrices and Determinants

Question Number 38282 by Tinkutara last updated on 23/Jun/18 Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jun/18 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 168339 by MikeH last updated on 09/Apr/22 $$\mathrm{A}\mathrm{point}\mathrm{in}\mathrm{rectangular}\mathrm{coordinates}$$$$(x,y,z)\mathrm{can}\mathrm{be}\mathrm{represented}\mathrm{in}\mathrm{spherical}$$$$\mathrm{coordinates}(r,\theta ,\phi )\mathrm{by}:$$$$x=r\sin \theta \sin \phi ,y=\sin \theta \sin \phi ,$$$$z=\sin \phi ,0⩽\theta ⩽2\pi ,0⩽\phi ⩽\pi$$$$\left(\mathrm{a}\right)\mathrm{Calculate}\mathrm{the}\mathrm{Jacobian}\mathrm{of}\mathrm{the}$$$$\mathrm{transformation}\frac{\partial (x,y,z)}{\partial (r,\theta ,\phi )}$$$$\left(\mathrm{b}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region} \…

Question Number 167183 by alcohol last updated on 09/Mar/22 Commented by ArielVyny last updated on 09/Mar/22 $$iletquestion\left(f\right)foryourattention$$ Answered by ArielVyny last updated on…

Question Number 35319 by Tinkutara last updated on 17/May/18 Answered by MJS last updated on 17/May/18 $${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{just}\mathrm{multiplicating}\mathrm{and}\mathrm{factorising}$$$$\det \left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|=aei+bfg+cdh-afh-bdi-ceg$$ Commented by Tinkutara last…

Question Number 100664 by bobhans last updated on 28/Jun/20 $$\mathrm{A}\mathrm{matrix}2\mathrm{\times }2\mathrm{\&}\mathrm{B}=\left(\begin{array}{c}-23\\ 24\end{array}\right)\mathrm{such}\mathrm{that}$$$${\mathrm{A}}^{\mathrm{T}}\mathrm{B}+{3\mathrm{A}}^{\mathrm{T}}=\left(\begin{array}{c}54\\ -11\end{array}\right)\mathrm{so}\mathrm{find}\det \left({4\mathrm{A}}^{-1}\right)$$ Answered by bramlex last updated on 28/Jun/20 $${A}^{{T}}…