Category: Matrices and Determinants

Question Number 64012 by aditya@345 last updated on 12/Jul/19 Answered by MJS last updated on 12/Jul/19 $$\left|\begin{array}{ccc}3& -2& \sin 3\theta \\ -7& 8& \cos 2\theta \\ -11& 14& 2\end{array}\right|=0$$$$20-20\cos 2\theta -10\sin 3\theta =0$$$$2\cos 2\theta +\sin 3\theta -2=0$$$$(1-2\sin \theta )(3+2\sin \theta )\sin \theta =0$$$$\mathrm{sin}\:\theta\:=−\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow\:\theta\notin\mathbb{R}…

Question Number 127541 by Study last updated on 30/Dec/20 $$canwefindthe4\times 4matricsinevers$$$$multiplicativematrics???$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 192464 by Engr_Jidda last updated on 18/May/23 Commented by a.lgnaoui last updated on 19/May/23 $$X^{\prime }?$$ Terms of Service Privacy Policy Contact:…

Question Number 60303 by Cheyboy last updated on 19/May/19 Answered by tw000001 last updated on 18/Oct/19 $$\det \left|\begin{array}{ccc}2& -1& 5\\ 3& 4& 0\\ -2& 1& 9\end{array}\right|=154$$$$\to {\left[\begin{array}{ccc}2& -1& 5\\ 3& 4& 0\\ -2& 1& 9\end{array}\right]}^{-1}=\left[\begin{array}{ccc}\frac{18}{77}& \frac{1}{11}& -\frac{10}{77}\\ -\frac{27}{154}& \frac{2}{11}& \frac{15}{154}\\ \frac{1}{14}& 0& \frac{1}{14}\end{array}\right]$$$$\det \left|\begin{array}{ccc}9& 7& 5\\ 1& 4& 3\\ 7& 5& -2\end{array}\right|=-161$$$$\rightarrow$$\left[\begin{array}{ccc}9& 7& 5\\ 1& 4& 3\\ 7& 5& -2\end{array}\right]$$^{−\mathrm{1}} =$$\left[\begin{array}{ccc}\frac{1}{7}& -\frac{39}{161}& -\frac{1}{161}\\ -\frac{1}{7}& \frac{53}{161}& \frac{22}{161}\\ \frac{1}{7}& -\frac{4}{161}& -\frac{29}{161}\end{array}\right]$$…

Question Number 191030 by cortano12 last updated on 16/Apr/23 Answered by Frix last updated on 16/Apr/23 $$t+\frac{1}{t}=3$$$${(t+\frac{1}{t})}^2=9\iff t^2+\frac{1}{t^2}=7$$$$\left({t}+\frac{\mathrm{1}}{{t}}\right)^{\mathrm{3}} =\mathrm{27}\:\Leftrightarrow\:{t}^{\mathrm{3}}…