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Category: Matrices and Determinants

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}}…

Let-is-value-of-characteristic-matrices-P-the-fill-P-t-P-2-find-all-the-posible-

Question Number 54969 by gunawan last updated on 15/Feb/19 $$\mathrm{Let}\:\lambda\:\mathrm{is}\:\mathrm{value}\:\mathrm{of}\:\mathrm{characteristic} \\ $$$$\mathrm{matrices}\:{P}\:\:\mathrm{the}\:\mathrm{fill}\:{P}^{{t}} ={P}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{all}\:\lambda\:\mathrm{the}\:\mathrm{posible} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Let-A-matrices-order-2-2-the-fill-tr-A-2-tr-A-2-a-Find-det-A-b-If-A-can-t-diagonalizing-find-tr-A-

Question Number 54968 by gunawan last updated on 15/Feb/19 $$\mathrm{Let}\:{A}\:\mathrm{matrices}\:\mathrm{order}\:\mathrm{2}×\mathrm{2}\:\mathrm{the}\:\mathrm{fill} \\ $$$$\mathrm{tr}\left({A}^{\mathrm{2}} \right)=\left[{tr}\left({A}\right)\right]^{\mathrm{2}} \\ $$$$\mathrm{a}.\:\mathrm{Find}\:\mathrm{det}\left(\mathrm{A}\right) \\ $$$$\mathrm{b}.\:\mathrm{If}\:\mathrm{A}\:\mathrm{can}'\mathrm{t}\:\mathrm{diagonalizing},\:\mathrm{find}\:\mathrm{tr}\left({A}\right) \\ $$$$ \\ $$ Answered by kaivan.ahmadi last…

Let-x-1-x-2-x-3-the-number-real-x-1-lt-x-2-lt-x-3-T-P-2-R-3-defined-with-rule-T-P-x-1-P-x-2-P-x-3-for-all-P-x-P-2-a-Prove-that-T-form-linear-transformation-b-

Question Number 54967 by gunawan last updated on 15/Feb/19 $$\mathrm{Let}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} \:\mathrm{the}\:\mathrm{number}\:\mathrm{real} \\ $$$${x}_{\mathrm{1}} <{x}_{\mathrm{2}} <{x}_{\mathrm{3}} .\:{T}\::\:{P}_{\mathrm{2}} \rightarrow{R}^{\mathrm{3}} \:\mathrm{defined} \\ $$$$\mathrm{with}\:\mathrm{rule}\:{T}=\begin{bmatrix}{{P}\left({x}_{\mathrm{1}} \right)}\\{{P}\left({x}_{\mathrm{2}} \right)}\\{{P}\left({x}_{\mathrm{3}} \right)}\end{bmatrix}…

Let-X-1-0-0-1-1-0-0-1-1-and-ortogonal-projection-at-X-Matrices-representation-P-to-basic-basis-in-space-Euclid-R-3-is-

Question Number 54962 by gunawan last updated on 15/Feb/19 $$\mathrm{Let}\:{X}=\left\{\left(−\mathrm{1},\:\mathrm{0},\:\mathrm{0}\right),\:\left(\mathrm{1},\:\mathrm{1},\:\mathrm{0}\right),\:\left(\mathrm{0},\:\mathrm{1},\:\mathrm{1}\right)\right. \\ $$$$\mathrm{and}\:\mathrm{ortogonal}\:\mathrm{projection}\:\mathrm{at}\:{X}. \\ $$$$\mathrm{Matrices}\:\mathrm{representation}\:\mathrm{P}\:\mathrm{to} \\ $$$$\mathrm{basic}\:\mathrm{basis}\:\mathrm{in}\:\mathrm{space}\:\mathrm{Euclid}\:\mathrm{R}^{\mathrm{3}} \:\mathrm{is}.. \\ $$ Terms of Service Privacy Policy Contact:…