Category: Matrices and Determinants

Question Number 194642 by horsebrand11 last updated on 12/Jul/23 $$\mathrm{If}\mathrm{A}=\left(\begin{array}{c}\mathrm{a}\mathrm{b}\mathrm{c}\\ \mathrm{b}\mathrm{c}\mathrm{a}\\ \mathrm{c}\mathrm{a}\mathrm{b}\end{array}\right)\mathrm{and}\mathrm{a},\mathrm{b},\mathrm{c}>0$$$$\mathrm{such}\mathrm{that}\mathrm{abc}=1\mathrm{and}{\mathrm{A}}^{\mathrm{T}}.\mathrm{A}=\mathrm{I}$$$$\mathrm{find}{\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3-3\mathrm{abc}.$$ Answered by som(math1967) last updated…

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Question Number 129886 by zarawan last updated on 23/Jan/21 $$FindNullspaceofthefollowingmatrixandalsofindbasisforthenullspace.$$$$\left[\begin{array}{ccccc}1& 1& 0& 0& 1\\ 0& 0& 1& -2& 0\\ 4& 2& 0& 0& 3\\ 1& 1& 1& -2& 1\\ 2& 2& 0& 0& 2\\ 1& 1& 2& 4& 1\end{array}\right]$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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}…