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Category: Matrices and Determinants

A-linear-transformation-E-of-the-x-y-plane-is-defined-as-E-x-y-2x-y-2x-3y-Find-the-equation-of-the-line-that-remains-invariant-under-the-transformation-

Question Number 183965 by nadovic last updated on 01/Jan/23 $$\mathrm{A}\:\mathrm{linear}\:\mathrm{transformation}\:\boldsymbol{{E}},\:\mathrm{of}\:\mathrm{the} \\ $$$${x}−{y}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{E}}:\left({x},\:{y}\right)\:\rightarrow\:\left(\mathrm{2}{x}+{y},\:\mathrm{2}{x}+\mathrm{3}{y}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{that} \\ $$$$\mathrm{remains}\:\mathrm{invariant}\:\mathrm{under}\:\mathrm{the} \\ $$$$\mathrm{transformation}. \\ $$ Answered by mr…

Question-183863

Question Number 183863 by Michaelfaraday last updated on 31/Dec/22 Answered by qaz last updated on 31/Dec/22 $$\frac{{d}}{{d}\theta}\left\{\begin{vmatrix}{\begin{pmatrix}{{A}}&{{B}}\\{{C}}&{{D}}\end{pmatrix}}&{\begin{pmatrix}{{E}}&{{F}}\\{{G}}&{{H}}\end{pmatrix}}\end{vmatrix}\right\} \\ $$$$=\frac{{d}}{{d}\theta}\left\{\begin{vmatrix}{{A}}&{{B}}\\{{C}}&{{D}}\end{vmatrix}\centerdot\begin{vmatrix}{{E}}&{{F}}\\{{G}}&{{H}}\end{vmatrix}\right\} \\ $$$$=\begin{vmatrix}{{A}}&{{B}}\\{{C}}&{{D}}\end{vmatrix}^{'} \centerdot\begin{vmatrix}{{E}}&{{F}}\\{{G}}&{{H}}\end{vmatrix}+\begin{vmatrix}{{A}}&{{B}}\\{{C}}&{{D}}\end{vmatrix}\centerdot\begin{vmatrix}{{E}}&{{F}}\\{{G}}&{{H}}\end{vmatrix}^{'} \\ $$$$=\left(\begin{vmatrix}{{A}'}&{{B}'}\\{{C}}&{{D}}\end{vmatrix}+\begin{vmatrix}{{A}}&{{B}}\\{{C}'}&{{D}'}\end{vmatrix}\right)\centerdot\begin{vmatrix}{{E}}&{{F}}\\{{G}}&{{H}}\end{vmatrix}+\begin{vmatrix}{{A}}&{{B}}\\{{C}}&{{D}}\end{vmatrix}\centerdot\left(\begin{vmatrix}{{E}'}&{{F}'}\\{{G}}&{{H}}\end{vmatrix}+\begin{vmatrix}{{E}}&{{F}}\\{{G}'}&{{H}'}\end{vmatrix}\right) \\…

determine-eigen-values-and-eigen-vectors-for-each-and-verify-Ax-x-A-3-2-1-2-1-2-3-2-

Question Number 183814 by ali009 last updated on 30/Dec/22 $${determine}\:{eigen}\:{values}\:{and}\:{eigen}\:{vectors}\:{for} \\ $$$${each}\:\lambda\:.\:{and}\:{verify}\:{Ax}=\lambda{x} \\ $$$${A}=\begin{bmatrix}{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}&{−\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}}&{\:\:\:\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\end{bmatrix} \\ $$ Answered by TheSupreme last updated on 30/Dec/22 $$\left\{{x}\right\}'={A}\left\{{x}\right\}\:{is}\:{a}\:{rotation}\:{of}\:\frac{\pi}{\mathrm{6}}\:{rads}\:{counterclockwise} \\…

Given-a-matrix-A-1-3-2-0-1-4-2-3-2-and-A-1-1-10-kA-9I-A-2-find-k-

Question Number 118231 by bemath last updated on 16/Oct/20 $${Given}\:{a}\:{matrix}\:{A}=\:\begin{pmatrix}{−\mathrm{1}\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{2}}\\{\:\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{4}}\\{−\mathrm{2}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$${and}\:{A}^{−\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{10}}\left({kA}+\mathrm{9}{I}−{A}^{\mathrm{2}} \right). \\ $$$${find}\:{k}. \\ $$ Answered by bobhans last updated on 16/Oct/20…

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Question Number 118090 by bemath last updated on 15/Oct/20 $$\mathrm{find}\:\begin{vmatrix}{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{c}}\:\:\:\:\:\:\:\:\mathrm{c}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}}\\{\:\:\:\:\:\mathrm{a}\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }{\mathrm{a}}\:\:\:\:\:\:\:\mathrm{a}}\\{\:\:\:\:\:\mathrm{b}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}\:\:\:\:\:\:\:\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }{\mathrm{b}}}\end{vmatrix}=?\: \\ $$ Commented by bemath last updated on 15/Oct/20…

consider-a-non-singular-2-2-square-matrix-T-If-trace-T-4-and-trace-T-2-5-what-is-determinant-of-the-matrix-T-

Question Number 117973 by bemath last updated on 14/Oct/20 $$\mathrm{consider}\:\mathrm{a}\:\mathrm{non}−\mathrm{singular}\:\mathrm{2}×\mathrm{2}\: \\ $$$$\mathrm{square}\:\mathrm{matrix}\:\mathrm{T}.\:\mathrm{If}\:\mathrm{trace}\:\left(\mathrm{T}\right)\:=\mathrm{4} \\ $$$$\mathrm{and}\:\mathrm{trace}\:\left(\mathrm{T}^{\mathrm{2}} \right)=\mathrm{5}\:\mathrm{what}\:\mathrm{is}\:\mathrm{determinant} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{T}\:? \\ $$ Answered by bobhans last updated on…

find-the-rank-of-the-matrix-A-and-B-by-following-row-operation-A-1-2-3-1-2-1-3-1-1-0-1-1-0-1-1-1-B-1-2-1-4-2-4-3-

Question Number 183425 by ali009 last updated on 25/Dec/22 $${find}\:{the}\:{rank}\:{of}\:{the}\:{matrix}\:{A}\:{and}\:{B}\:{by} \\ $$$$\:{following}\:{row}\:{operation}: \\ $$$${A}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{2}}&{−\mathrm{1}}&{−\mathrm{3}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix} \\ $$$${B}=\begin{bmatrix}{\:\:\:\:\mathrm{1}}&{\:\:\:\:\mathrm{2}}&{−\mathrm{1}}&{\:\:\:\:\:\mathrm{4}}\\{\:\:\:\:\mathrm{2}}&{\:\:\:\:\mathrm{4}}&{\:\:\:\:\:\mathrm{3}}&{\:\:\:\:\:\mathrm{5}}\\{−\mathrm{1}}&{−\mathrm{2}}&{\:\:\:\:\:\mathrm{6}}&{−\mathrm{7}}\end{bmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

find-the-value-of-cofficent-in-the-following-system-from-the-determinat-2x-1-x-2-x-3-0-1-x-1-x-2-2x-3-0-4x-1-x-2-4x-3-0-

Question Number 183240 by ali009 last updated on 23/Dec/22 $${find}\:{the}\:{value}\:{of}\:{cofficent}\:\mu\:{in}\:{the}\:{following} \\ $$$${system}\:{from}\:{the}\:{determinat}: \\ $$$$\mathrm{2}{x}_{\mathrm{1}} +\mu{x}_{\mathrm{2}} +{x}_{\mathrm{3}} =\mathrm{0} \\ $$$$\left(\mu−\mathrm{1}\right){x}_{\mathrm{1}} −{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} =\mathrm{0} \\ $$$$\mathrm{4}{x}_{\mathrm{1}} +{x}^{\mathrm{2}}…