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Category: Matrices and Determinants

Question-56510

Question Number 56510 by Tawa1 last updated on 17/Mar/19 Commented by MJS last updated on 17/Mar/19 $$\mathrm{well},\:\mathrm{the}\:\mathrm{determinant}\:\mathrm{is} \\ $$$$\mathrm{2}{a}^{\mathrm{4}} {bc}+\mathrm{2}{ab}^{\mathrm{4}} {c}+\mathrm{2}{abc}^{\mathrm{4}} +\mathrm{6}{a}^{\mathrm{3}} {b}^{\mathrm{2}} {c}+\mathrm{6}{a}^{\mathrm{3}} {bc}^{\mathrm{2}}…

Given-A-a-3×3-matrix-satisfy-A-1-2-3-3-4-2-A-5-9-7-3-1-2-Find-A-10-18-14-

Question Number 121523 by benjo_mathlover last updated on 09/Nov/20 $$\mathrm{Given}\:\mathrm{A}\:\mathrm{a}\:\mathrm{3×3}\:\mathrm{matrix}\:\mathrm{satisfy}\: \\ $$$$\rightarrow\begin{cases}{\mathrm{A}\begin{pmatrix}{\mathrm{1}}\\{\mathrm{2}}\\{\mathrm{3}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}}\\{\mathrm{A}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{9}}\\{\mathrm{7}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\\{\mathrm{2}}\end{pmatrix}}\end{cases} \\ $$$$.\:\mathrm{Find}\:\mathrm{A}\begin{pmatrix}{\mathrm{10}}\\{\mathrm{18}}\\{\mathrm{14}}\end{pmatrix}\:?\: \\ $$ Commented by liberty last updated on 09/Nov/20 $$\Leftrightarrow\:\mathrm{A}\begin{pmatrix}{\mathrm{10}}\\{\mathrm{18}}\\{\mathrm{14}}\end{pmatrix}\:=\:\mathrm{2A}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{9}}\\{\mathrm{7}}\end{pmatrix}\:=\:\mathrm{2}\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\\{\mathrm{2}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{6}}\\{\mathrm{2}}\\{\mathrm{4}}\end{pmatrix} \\…

Given-matrices-A-x-x-1-3-4-x-3-M-2-R-The-smallest-det-A-x-is-

Question Number 55374 by gunawan last updated on 23/Feb/19 $$\mathrm{Given}\:\mathrm{matrices}\:{A}\left({x}\right)=\begin{bmatrix}{{x}−\mathrm{1}}&{\mathrm{3}}\\{\mathrm{4}}&{{x}+\mathrm{3}}\end{bmatrix}\in\:{M}_{\mathrm{2}} \left(\mathbb{R}\right). \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{det}\left({A}\left({x}\right)\right)\:\mathrm{is}.. \\ $$ Answered by Joel578 last updated on 23/Feb/19 $$\mid{A}\left({x}\right)\mid\:=\:\left({x}\:−\:\mathrm{1}\right)\left({x}\:+\:\mathrm{3}\right)\:−\:\mathrm{12} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{x}^{\mathrm{2}}…